tag:blogger.com,1999:blog-67793409573462722252024-02-08T07:48:38.624-08:00BAHAN AJAR MATEMATIKA SMAMASKUN-WONG-PERJAhttp://www.blogger.com/profile/10525088792966143650noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-6779340957346272225.post-54123010921338402422011-12-10T04:34:00.001-08:002011-12-10T22:38:52.810-08:00Bahan Ajar Matematika Power PointBerikut ini saya buatkan bahan ajar Matematika dengan power point semoga bermanfaat bagi perkembangan Matematika di negeri tercinta ini<span style="color: blue; font-size: large;"> <span style="color: red;">Silakan download link berikut :</span></span><br />
<ul>
<li><span style="color: blue; font-size: large;">KELAS X</span></li>
</ul>
<ul>
<li><a href="http://www.mediafire.com/?xao5yzmqg83jm">Bilangan Berpangkat dan logaritma</a></li>
<li><a href="http://www.mediafire.com/?9bgpakwru8kmb">Persamaan Kuadrat</a></li>
<li><a href="http://www.mediafire.com/?wp0643ba1bmkg">SPL</a></li>
<li><a href="http://www.mediafire.com/?8uk8zg4fgze8r">Logika Matematika</a></li>
<li><a href="http://www.mediafire.com/?l8jsgrc2k609i">Trigonometri</a></li>
<li><a href="http://www.mediafire.com/?dmxgwmiyz76fs">Dimensi Tiga</a><span style="color: blue; font-size: large;"> </span></li>
</ul>
<ul>
<li><span style="color: blue; font-size: large;"> </span><span style="color: blue; font-size: large;">KELAS XI</span></li>
</ul>
<ul>
<li> <a href="http://www.mediafire.com/?048s30y4n0lnr">Statistik</a></li>
<li><a href="http://www.mediafire.com/?jsp25faw9bicn">Peluang</a></li>
<li><a href="http://www.mediafire.com/?qznm1y77nnmpw">Lingkaran</a></li>
<li> <a href="http://www.mediafire.com/?563by1c4grfdz">Suku Banyak</a></li>
<li> <a href="http://www.mediafire.com/?3bvwr8ukh69vq">Komposisi Fungsi</a></li>
<li><a href="http://www.mediafire.com/?kcvu6jh30pziu">Limit</a></li>
<li><a href="http://www.mediafire.com/?i3ssa8o4z06fd">Trigonometri</a><a href="http://www.blogger.com/goog_1216465586"> </a></li>
<li><a href="http://www.mediafire.com/?5in9gjmqme755">Turunan</a></li>
</ul>
<br />
<ul>
<li><span style="color: blue; font-size: large;"> </span><span style="color: blue; font-size: large;">KELAS XII</span></li>
</ul>
<ul>
<li> <a href="http://www.mediafire.com/?vuzuuyjwlyo6c">Integral</a></li>
<li><a href="http://www.mediafire.com/?vu8bi7uxi2w5q">Program Linear</a></li>
<li><a href="http://www.mediafire.com/?qn02b30sc8kz3">Vektor</a></li>
<li><a href="http://www.mediafire.com/?fbn0pka2jisdl">Transformasi Geometri</a></li>
<li><a href="http://www.mediafire.com/?h7trkj3k63ru4">Matriks</a></li>
<li><a href="http://www.mediafire.com/?zyyeatl2b577a">Barisan dan Deret</a></li>
</ul>
<ul> </ul>MASKUN-WONG-PERJAhttp://www.blogger.com/profile/10525088792966143650noreply@blogger.com0tag:blogger.com,1999:blog-6779340957346272225.post-7191420472227946282011-12-09T23:29:00.001-08:002011-12-09T23:30:49.145-08:00INTEGRAL SUBSTITUSI<h3 class="post-title entry-title">
Integral Substitusi
</h3>
<div class="post-header">
</div>
Dalam pengintegralan kita sering kesulitan karena masalah fungsi,
misalkan adanya pangkat yang tinggi, bentuk akar, serta fungsi-fungi
trigonometri. Untuk itu maka digunakan penggantian, atau disebut
substitusi. karena itulah pada langkah ini dilakukan pemisalan.<br /><a name='more'></a><br />Contoh :<br /><a href="http://www.codecogs.com/eqnedit.php?latex=1.%20%5Cint%20%5Cleft%20%28%203x-4%20%5Cright%20%29%5E%7B10%7Ddx=..." target="_blank"><img src="http://latex.codecogs.com/gif.latex?1.%20%5Cint%20%5Cleft%20%28%203x-4%20%5Cright%20%29%5E%7B10%7Ddx=..." title="1. \int \left ( 3x-4 \right )^{10}dx=..." /></a><br /><br />dari bentuk ini yang kita lakukan adalah dengan memisalkan<br />misal y = 3x - 4<br />maka<br /><a href="http://www.codecogs.com/eqnedit.php?latex=%5Cfrac%7Bdy%7D%7Bdx%7D=3" target="_blank"><img src="http://latex.codecogs.com/gif.latex?%5Cfrac%7Bdy%7D%7Bdx%7D=3" title="\frac{dy}{dx}=3" /></a><br />sehingga<br /><a href="http://www.codecogs.com/eqnedit.php?latex=dx=%5Cfrac%7Bdy%7D%7B3%7D" target="_blank"><img src="http://latex.codecogs.com/gif.latex?dx=%5Cfrac%7Bdy%7D%7B3%7D" title="dx=\frac{dy}{3}" /></a><br />Jadi, bentuk integral menjadi<br /><br /><a href="http://www.codecogs.com/eqnedit.php?latex=%5Cint%20%5Cleft%20%28%203x-4%20%5Cright%20%29%5E%7B10%7Ddx=%5Cint%20y%5E%7B10%7D%5Cfrac%7Bdy%7D%7B3%7D=%5Cfrac%7B1%7D%7B3%7D%5Cint%20y%5E%7B10%7Ddy=%5Cfrac%7B1%7D%7B3%7D.%5Cfrac%7B1%7D%7B11%7Dy%5E%7B11%7D@plus;c" target="_blank"><img src="http://latex.codecogs.com/gif.latex?%5Cint%20%5Cleft%20%28%203x-4%20%5Cright%20%29%5E%7B10%7Ddx=%5Cint%20y%5E%7B10%7D%5Cfrac%7Bdy%7D%7B3%7D=%5Cfrac%7B1%7D%7B3%7D%5Cint%20y%5E%7B10%7Ddy=%5Cfrac%7B1%7D%7B3%7D.%5Cfrac%7B1%7D%7B11%7Dy%5E%7B11%7D+c" title="\int \left ( 3x-4 \right )^{10}dx=\int y^{10}\frac{dy}{3}=\frac{1}{3}\int y^{10}dy=\frac{1}{3}.\frac{1}{11}y^{11}+c" /></a><br /><a href="http://www.codecogs.com/eqnedit.php?latex==%5Cfrac%7B1%7D%7B33%7D%5Cleft%20%28%203x-4%20%5Cright%20%29%5E%7B11%7D@plus;c" target="_blank"><img src="http://latex.codecogs.com/gif.latex?=%5Cfrac%7B1%7D%7B33%7D%5Cleft%20%28%203x-4%20%5Cright%20%29%5E%7B11%7D+c" title="=\frac{1}{33}\left ( 3x-4 \right )^{11}+c" /></a><br /><br /><b> contoh 2</b><br /><a href="http://www.codecogs.com/eqnedit.php?latex=%5Cint%20x%5Cleft%20%28%20x%5E%7B2%7D@plus;6%20%5Cright%20%29%5E%7B14%7Ddx=..." target="_blank"><img src="http://latex.codecogs.com/gif.latex?%5Cint%20x%5Cleft%20%28%20x%5E%7B2%7D+6%20%5Cright%20%29%5E%7B14%7Ddx=..." title="\int x\left ( x^{2}+6 \right )^{14}dx=..." /></a><br />misal :<br />y = x<sup>2</sup> + 6<br />maka<br /><a href="http://www.codecogs.com/eqnedit.php?latex=%5Cfrac%7Bdy%7D%7Bdx%7D=2x" target="_blank"><img src="http://latex.codecogs.com/gif.latex?%5Cfrac%7Bdy%7D%7Bdx%7D=2x" title="\frac{dy}{dx}=2x" /></a><br />sehingga<br /><a href="http://www.codecogs.com/eqnedit.php?latex=dx=%5Cfrac%7Bdy%7D%7B2x%7D" target="_blank"><img src="http://latex.codecogs.com/gif.latex?dx=%5Cfrac%7Bdy%7D%7B2x%7D" title="dx=\frac{dy}{2x}" /></a><br />Jadi :<br /><br /><a href="http://www.codecogs.com/eqnedit.php?latex=%5Cint%20x%5Cleft%20%28%20x%5E%7B2%7D@plus;6%20%5Cright%20%29%5E%7B14%7Ddx=%5Cint%20xy%5E%7B14%7D%5Cfrac%7Bdy%7D%7B2x%7D=%5Cfrac%7B1%7D%7B2%7D%5Cint%20y%5E%7B14%7Ddy=%5Cfrac%7B1%7D%7B2%7D.%5Cfrac%7B1%7D%7B15%7Dy%5E%7B15%7D@plus;c" target="_blank"><img src="http://latex.codecogs.com/gif.latex?%5Cint%20x%5Cleft%20%28%20x%5E%7B2%7D+6%20%5Cright%20%29%5E%7B14%7Ddx=%5Cint%20xy%5E%7B14%7D%5Cfrac%7Bdy%7D%7B2x%7D=%5Cfrac%7B1%7D%7B2%7D%5Cint%20y%5E%7B14%7Ddy=%5Cfrac%7B1%7D%7B2%7D.%5Cfrac%7B1%7D%7B15%7Dy%5E%7B15%7D+c" title="\int x\left ( x^{2}+6 \right )^{14}dx=\int xy^{14}\frac{dy}{2x}=\frac{1}{2}\int y^{14}dy=\frac{1}{2}.\frac{1}{15}y^{15}+c" /></a><br /><br /><a href="http://www.codecogs.com/eqnedit.php?latex==%20%5Cfrac%7B1%7D%7B30%7D%5Cleft%20%28%20x%5E%7B2%7D@plus;6%20%5Cright%20%29%5E%7B15%7D@plus;c" target="_blank"><img src="http://latex.codecogs.com/gif.latex?=%20%5Cfrac%7B1%7D%7B30%7D%5Cleft%20%28%20x%5E%7B2%7D+6%20%5Cright%20%29%5E%7B15%7D+c" title="= \frac{1}{30}\left ( x^{2}+6 \right )^{15}+c" /></a><br /><a href="http://web-matematika.blogspot.com/2010/08/integral-tak-tentu-2.html"><br /></a><h3 class="post-title entry-title">
Integral Substitusi 2
</h3>
<div class="post-header">
</div>
<span style="font-size: 130%; font-weight: bold;">Contoh 2 :</span><br /><a href="http://www.codecogs.com/eqnedit.php?latex=%5Cint%20x%5Cleft%20%28%20x%5E%7B2%7D@plus;8%20%5Cright%20%29%5E%7B19%7Ddx%20=%20..." target="_blank"><img src="http://latex.codecogs.com/gif.latex?%5Cint%20x%5Cleft%20%28%20x%5E%7B2%7D+8%20%5Cright%20%29%5E%7B19%7Ddx%20=%20..." title="\int x\left ( x^{2}+8 \right )^{19}dx = ..." /></a><br /><br /><span style="font-size: 130%; font-weight: bold;">Jawab :</span><br />Misal y = x<sup>2</sup> + 8<br />maka<br /><a href="http://www.codecogs.com/eqnedit.php?latex=%5Cfrac%7Bdy%7D%7Bdx%7D=2x" target="_blank"><img src="http://latex.codecogs.com/gif.latex?%5Cfrac%7Bdy%7D%7Bdx%7D=2x" title="\frac{dy}{dx}=2x" /></a><br />Sehingga<br /><a href="http://www.codecogs.com/eqnedit.php?latex=dx=%5Cfrac%7Bdy%7D%7B2x%7D" target="_blank"><img src="http://latex.codecogs.com/gif.latex?dx=%5Cfrac%7Bdy%7D%7B2x%7D" title="dx=\frac{dy}{2x}" /></a><br /><br />Maka<br /><a href="http://www.codecogs.com/eqnedit.php?latex=%5Cint%20x%5Cleft%20%28%20x%5E%7B2%7D@plus;8%20%5Cright%20%29%5E%7B19%7Ddx%20=%20%5Cint%20xy%5E%7B19%7D%5Cfrac%7Bdy%7D%7B2x%7D=%5Cfrac%7B1%7D%7B2%7D%5Cint%20y%5E%7B19%7Ddy" target="_blank"><img src="http://latex.codecogs.com/gif.latex?%5Cint%20x%5Cleft%20%28%20x%5E%7B2%7D+8%20%5Cright%20%29%5E%7B19%7Ddx%20=%20%5Cint%20xy%5E%7B19%7D%5Cfrac%7Bdy%7D%7B2x%7D=%5Cfrac%7B1%7D%7B2%7D%5Cint%20y%5E%7B19%7Ddy" title="\int x\left ( x^{2}+8 \right )^{19}dx = \int xy^{19}\frac{dy}{2x}=\frac{1}{2}\int y^{19}dy" /></a><br /><a href="http://www.codecogs.com/eqnedit.php?latex==%20%5Cfrac%7B1%7D%7B2%7D.%5Cfrac%7B1%7D%7B20%7Dy%5E%7B20%7D%20@plus;%20c%20=%20%5Cfrac%7B1%7D%7B40%7D%5Cleft%20%28%20x%5E%7B2%7D%20@plus;%208%20%5Cright%20%29%5E%7B20%7D%20@plus;%20c" target="_blank"><img src="http://latex.codecogs.com/gif.latex?=%20%5Cfrac%7B1%7D%7B2%7D.%5Cfrac%7B1%7D%7B20%7Dy%5E%7B20%7D%20+%20c%20=%20%5Cfrac%7B1%7D%7B40%7D%5Cleft%20%28%20x%5E%7B2%7D%20+%208%20%5Cright%20%29%5E%7B20%7D%20+%20c" title="= \frac{1}{2}.\frac{1}{20}y^{20} + c = \frac{1}{40}\left ( x^{2} + 8 \right )^{20} + c" /></a><br /><br /><span style="font-size: 130%;"><span style="font-weight: bold;">Contoh 3 :</span></span><br /><a href="http://www.codecogs.com/eqnedit.php?latex=%5Cint%20x%5E%7B3%7D%5Cleft%20%28%20x%5E%7B4%7D%20-%2012%20%5Cright%20%29%5E%7B24%7D%20dx%20=%20..." target="_blank"><img src="http://latex.codecogs.com/gif.latex?%5Cint%20x%5E%7B3%7D%5Cleft%20%28%20x%5E%7B4%7D%20-%2012%20%5Cright%20%29%5E%7B24%7D%20dx%20=%20..." title="\int x^{3}\left ( x^{4} - 12 \right )^{24} dx = ..." /></a><br /><br /><span style="font-size: 130%;"><span style="font-weight: bold;">Jawab :</span></span><br />misal y = x<sup>4</sup> - 12<br />maka<br /><a href="http://www.codecogs.com/eqnedit.php?latex=%5Cfrac%7Bdy%7D%7Bdx%7D=%204x%5E%7B3%7D" target="_blank"><img src="http://latex.codecogs.com/gif.latex?%5Cfrac%7Bdy%7D%7Bdx%7D=%204x%5E%7B3%7D" title="\frac{dy}{dx}= 4x^{3}" /></a><br />Akibatnya<br /><a href="http://www.codecogs.com/eqnedit.php?latex=dx=%5Cfrac%7Bdy%7D%7B4x%5E%7B3%7D%7D" target="_blank"><img src="http://latex.codecogs.com/gif.latex?dx=%5Cfrac%7Bdy%7D%7B4x%5E%7B3%7D%7D" title="dx=\frac{dy}{4x^{3}}" /></a><br />jadi<br /><br /><a href="http://www.codecogs.com/eqnedit.php?latex=%5Cint%20x%5E%7B3%7D%5Cleft%20%28%20x%5E%7B4%7D-12%20%5Cright%20%29%5E%7B24%7Ddx%20=%20%5Cint%20x%5E%7B3%7Dy%5E%7B24%7D%5Cfrac%7Bdy%7D%7B4x%5E%7B3%7D%7D=%5Cfrac%7B1%7D%7B4%7D%5Cint%20y%5E%7B24%7Ddy" target="_blank"><img src="http://latex.codecogs.com/gif.latex?%5Cint%20x%5E%7B3%7D%5Cleft%20%28%20x%5E%7B4%7D-12%20%5Cright%20%29%5E%7B24%7Ddx%20=%20%5Cint%20x%5E%7B3%7Dy%5E%7B24%7D%5Cfrac%7Bdy%7D%7B4x%5E%7B3%7D%7D=%5Cfrac%7B1%7D%7B4%7D%5Cint%20y%5E%7B24%7Ddy" title="\int x^{3}\left ( x^{4}-12 \right )^{24}dx = \int x^{3}y^{24}\frac{dy}{4x^{3}}=\frac{1}{4}\int y^{24}dy" /></a><br /><a href="http://www.codecogs.com/eqnedit.php?latex=%5Cfrac%7B1%7D%7B4%7D.%5Cfrac%7B1%7D%7B25%7Dy%5E%7B25%7D@plus;%20c%20=%20%5Cfrac%7B1%7D%7B100%7D%5Cleft%20%28%20x%5E%7B4%7D%20-%2012%20%5Cright%20%29%20@plus;%20c" target="_blank"><img src="http://latex.codecogs.com/gif.latex?%5Cfrac%7B1%7D%7B4%7D.%5Cfrac%7B1%7D%7B25%7Dy%5E%7B25%7D+%20c%20=%20%5Cfrac%7B1%7D%7B100%7D%5Cleft%20%28%20x%5E%7B4%7D%20-%2012%20%5Cright%20%29%20+%20c" title="\frac{1}{4}.\frac{1}{25}y^{25}+ c = \frac{1}{100}\left ( x^{4} - 12 \right ) + c" /></a><br /><br /><h3 class="post-title entry-title">
Integral Substitusi 3
</h3>
<div class="post-header">
</div>
<span style="font-size: 130%; font-weight: bold;">Contoh 4</span><br />Hitunglah Integral Berikut<br /><a href="http://www.codecogs.com/eqnedit.php?latex=%5Cint%20%5Cleft%20%28%20x@plus;3%20%5Cright%20%29%5Cleft%20%28%20x%5E%7B2%7D@plus;6x@plus;5%20%5Cright%20%29%5E%7B12%7Ddx=..." target="_blank"><img src="http://latex.codecogs.com/gif.latex?%5Cint%20%5Cleft%20%28%20x+3%20%5Cright%20%29%5Cleft%20%28%20x%5E%7B2%7D+6x+5%20%5Cright%20%29%5E%7B12%7Ddx=..." title="\int \left ( x+3 \right )\left ( x^{2}+6x+5 \right )^{12}dx=..." /></a><br /><br /><span style="font-size: 130%; font-weight: bold;">Jawab :</span><br />misal y = x<sup>2</sup> + 6x + 5<br />maka<br /><a href="http://www.codecogs.com/eqnedit.php?latex=%5Cfrac%7Bdy%7D%7Bdx%7D=2x@plus;6" target="_blank"><img src="http://latex.codecogs.com/gif.latex?%5Cfrac%7Bdy%7D%7Bdx%7D=2x+6" title="\frac{dy}{dx}=2x+6" /></a><br />sehingga<br /><a href="http://www.codecogs.com/eqnedit.php?latex=dx=%5Cfrac%7Bdy%7D%7B2x@plus;6%7D=%5Cfrac%7Bdy%7D%7B2%28x@plus;3%29%7D" target="_blank"><img src="http://latex.codecogs.com/gif.latex?dx=%5Cfrac%7Bdy%7D%7B2x+6%7D=%5Cfrac%7Bdy%7D%7B2%28x+3%29%7D" title="dx=\frac{dy}{2x+6}=\frac{dy}{2(x+3)}" /></a><br />Jadi :<br /><a href="http://www.codecogs.com/eqnedit.php?latex=%5Cint%20%5Cleft%20%28%20x@plus;3%20%5Cright%20%29%5Cleft%20%28%20x%5E%7B2%7D@plus;6x@plus;5%20%5Cright%20%29%5E%7B12%7Ddx%20=%5Cint%20%5Cleft%20%28%20x@plus;3%20%5Cright%20%29y%5E%7B12%7D%5Cfrac%7Bdy%7D%7B2%28x@plus;3%29%7D=%5Cfrac%7B1%7D%7B2%7D%5Cint%20y%5E%7B12%7Ddy" target="_blank"><img src="http://latex.codecogs.com/gif.latex?%5Cint%20%5Cleft%20%28%20x+3%20%5Cright%20%29%5Cleft%20%28%20x%5E%7B2%7D+6x+5%20%5Cright%20%29%5E%7B12%7Ddx%20=%5Cint%20%5Cleft%20%28%20x+3%20%5Cright%20%29y%5E%7B12%7D%5Cfrac%7Bdy%7D%7B2%28x+3%29%7D=%5Cfrac%7B1%7D%7B2%7D%5Cint%20y%5E%7B12%7Ddy" title="\int \left ( x+3 \right )\left ( x^{2}+6x+5 \right )^{12}dx =\int \left ( x+3 \right )y^{12}\frac{dy}{2(x+3)}=\frac{1}{2}\int y^{12}dy" /></a><br /><br /><a href="http://www.codecogs.com/eqnedit.php?latex==%5Cfrac%7B1%7D%7B2%7D.%5Cfrac%7B1%7D%7B13%7Dy%5E%7B13%7D@plus;c=%5Cfrac%7B1%7D%7B26%7D%28x%5E%7B2%7D@plus;6x@plus;5%29%5E%7B13%7D@plus;c" target="_blank"><img src="http://latex.codecogs.com/gif.latex?=%5Cfrac%7B1%7D%7B2%7D.%5Cfrac%7B1%7D%7B13%7Dy%5E%7B13%7D+c=%5Cfrac%7B1%7D%7B26%7D%28x%5E%7B2%7D+6x+5%29%5E%7B13%7D+c" title="=\frac{1}{2}.\frac{1}{13}y^{13}+c=\frac{1}{26}(x^{2}+6x+5)^{13}+c" /></a><br /><br /><span style="font-size: 130%; font-weight: bold;">Contoh 5 :</span><br />Carilah hasil integral berikut<br /><a href="http://www.codecogs.com/eqnedit.php?latex=%5Cint%20%28x%5E%7B2%7D-1%29%5Csqrt%7Bx%5E%7B3%7D-3x@plus;5%7Ddx=..." target="_blank"><img src="http://latex.codecogs.com/gif.latex?%5Cint%20%28x%5E%7B2%7D-1%29%5Csqrt%7Bx%5E%7B3%7D-3x+5%7Ddx=..." title="\int (x^{2}-1)\sqrt{x^{3}-3x+5}dx=..." /></a><br /><br /><span style="font-size: 130%;"><span style="font-weight: bold;">Jawab :</span></span><br />misal : y = x<sup>3</sup>-3x+5<br />sehingga<br /><a href="http://www.codecogs.com/eqnedit.php?latex=%5Cfrac%7Bdy%7D%7Bdx%7D=3x%5E%7B2%7D-3" target="_blank"><img src="http://latex.codecogs.com/gif.latex?%5Cfrac%7Bdy%7D%7Bdx%7D=3x%5E%7B2%7D-3" title="\frac{dy}{dx}=3x^{2}-3" /></a><br />maka<br /><a href="http://www.codecogs.com/eqnedit.php?latex=dx=%5Cfrac%7Bdy%7D%7B3x%5E%7B2%7D-3%7D=%5Cfrac%7Bdy%7D%7B3%28x%5E%7B2%7D-1%29%7D" target="_blank"><img src="http://latex.codecogs.com/gif.latex?dx=%5Cfrac%7Bdy%7D%7B3x%5E%7B2%7D-3%7D=%5Cfrac%7Bdy%7D%7B3%28x%5E%7B2%7D-1%29%7D" title="dx=\frac{dy}{3x^{2}-3}=\frac{dy}{3(x^{2}-1)}" /></a><br />Dengan demikian<br /><a href="http://www.codecogs.com/eqnedit.php?latex=%5Cint%20%28x%5E%7B2%7D-1%29%5Csqrt%7Bx%5E%7B3%7D-3x@plus;5%7Ddx%20=%20%5Cint%20%28x%5E%7B2%7D-1%29%5Csqrt%7By%7D.%5Cfrac%7Bdy%7D%7B3%28x%5E%7B2%7D-1%29%7D=%5Cfrac%7B1%7D%7B3%7D%5Cint%20y%5E%7B%5Cfrac%7B1%7D%7B2%7D%7Ddy" target="_blank"><img src="http://latex.codecogs.com/gif.latex?%5Cint%20%28x%5E%7B2%7D-1%29%5Csqrt%7Bx%5E%7B3%7D-3x+5%7Ddx%20=%20%5Cint%20%28x%5E%7B2%7D-1%29%5Csqrt%7By%7D.%5Cfrac%7Bdy%7D%7B3%28x%5E%7B2%7D-1%29%7D=%5Cfrac%7B1%7D%7B3%7D%5Cint%20y%5E%7B%5Cfrac%7B1%7D%7B2%7D%7Ddy" title="\int (x^{2}-1)\sqrt{x^{3}-3x+5}dx = \int (x^{2}-1)\sqrt{y}.\frac{dy}{3(x^{2}-1)}=\frac{1}{3}\int y^{\frac{1}{2}}dy" /></a><br /><a href="http://www.codecogs.com/eqnedit.php?latex==%5Cfrac%7B1%7D%7B3%7D.%5Cfrac%7B2%7D%7B3%7Dy%5E%7B%5Cfrac%7B3%7D%7B2%7D%7D@plus;c=%5Cfrac%7B2%7D%7B9%7D%5Cleft%20%28%20x%5E%7B3%7D-3x@plus;5%20%5Cright%20%29%5E%7B%5Cfrac%7B3%7D%7B2%7D%7D@plus;c" target="_blank"><img src="http://latex.codecogs.com/gif.latex?=%5Cfrac%7B1%7D%7B3%7D.%5Cfrac%7B2%7D%7B3%7Dy%5E%7B%5Cfrac%7B3%7D%7B2%7D%7D+c=%5Cfrac%7B2%7D%7B9%7D%5Cleft%20%28%20x%5E%7B3%7D-3x+5%20%5Cright%20%29%5E%7B%5Cfrac%7B3%7D%7B2%7D%7D+c" title="=\frac{1}{3}.\frac{2}{3}y^{\frac{3}{2}}+c=\frac{2}{9}\left ( x^{3}-3x+5 \right )^{\frac{3}{2}}+c" /></a><br /><br /><span style="font-size: 180%;"></span>MASKUN-WONG-PERJAhttp://www.blogger.com/profile/10525088792966143650noreply@blogger.com0tag:blogger.com,1999:blog-6779340957346272225.post-192555671433794302011-12-09T23:26:00.001-08:002011-12-09T23:28:01.566-08:00INTEGRAL TRIGONOMETRI<h3 class="post-title entry-title">
Integral Trigonometri
</h3>
<div class="post-header">
</div>
<div class="post-body entry-content" id="post-body-1377706183739628058">
Integral Trigonometri merupakan hasil kebalikan dari turunan
trigonometri. Sebelum kita mencoba mengingat rumus-rumus integral
triogonometri maka sebaiknya kita ingat dulu turunan trigonometri.
Turunan trigonometri bisa kita tuliskan sebagai berikut<br />y = sin x maka y' = cos x<br />y = cos x maka y' = - sin x<br />y = tan x maka y' = sec<sup>2</sup> x<br />y = cot x maka y' = -csc<sup>2</sup> x<br />y = sec x maka y' = sec x tan x<br />y = csc x maka y' = -csc x cot x</div>
<div class="post-body entry-content" id="post-body-1377706183739628058">
<br /><a name='more'></a><br />Dengan demikian jika rumus-rumus ini kita balik akan menjadi<br /><a href="http://www.codecogs.com/eqnedit.php?latex=%5Cint%20cos%20x%20dx%20=%20sin%20x%20@plus;%20c" target="_blank"><img src="http://latex.codecogs.com/gif.latex?%5Cint%20cos%20x%20dx%20=%20sin%20x%20+%20c" title="\int cos x dx = sin x + c" /></a><br /><a href="http://www.codecogs.com/eqnedit.php?latex=%5Cint%20sin%20x%20dx%20=%20-cos%20x%20@plus;%20c" target="_blank"><img src="http://latex.codecogs.com/gif.latex?%5Cint%20sin%20x%20dx%20=%20-cos%20x%20+%20c" title="\int sin x dx = -cos x + c" /></a><br /><a href="http://www.codecogs.com/eqnedit.php?latex=%5Cint%20sec%5E%7B2%7D%20x%20dx%20=%20tan%20x%20@plus;%20c" target="_blank"><img src="http://latex.codecogs.com/gif.latex?%5Cint%20sec%5E%7B2%7D%20x%20dx%20=%20tan%20x%20+%20c" title="\int sec^{2} x dx = tan x + c" /></a><br /><a href="http://www.codecogs.com/eqnedit.php?latex=%5Cint%20csc%5E%7B2%7D%20x%20dx%20=%20-cot%20x%20@plus;%20c" target="_blank"><img src="http://latex.codecogs.com/gif.latex?%5Cint%20csc%5E%7B2%7D%20x%20dx%20=%20-cot%20x%20+%20c" title="\int csc^{2} x dx = -cot x + c" /></a><br /><a href="http://www.codecogs.com/eqnedit.php?latex=%5Cint%20sec%20x%20tan%20x%20dx%20=%20sec%20x%20@plus;%20c" target="_blank"><img src="http://latex.codecogs.com/gif.latex?%5Cint%20sec%20x%20tan%20x%20dx%20=%20sec%20x%20+%20c" title="\int sec x tan x dx = sec x + c" /></a><br /><a href="http://www.codecogs.com/eqnedit.php?latex=%5Cint%20csc%20x%20cot%20x%20dx%20=%20-csc%20x%20@plus;%20c" target="_blank"><img src="http://latex.codecogs.com/gif.latex?%5Cint%20csc%20x%20cot%20x%20dx%20=%20-csc%20x%20+%20c" title="\int csc x cot x dx = -csc x + c" /></a><br /><br />Rumus-rumus tersebut bisa dibuat lebih umum sebagai berikut<br /><a href="http://www.codecogs.com/eqnedit.php?latex=%5Cint%20cos%20%28ax@plus;b%29%20dx%20=%20%5Cfrac%7B1%7D%7Ba%7Dsin%28ax@plus;b%29%20@plus;%20c" target="_blank"><img src="http://latex.codecogs.com/gif.latex?%5Cint%20cos%20%28ax+b%29%20dx%20=%20%5Cfrac%7B1%7D%7Ba%7Dsin%28ax+b%29%20+%20c" title="\int cos (ax+b) dx = \frac{1}{a}sin(ax+b) + c" /></a><br /><a href="http://www.codecogs.com/eqnedit.php?latex=%5Cint%20sin%20%28ax@plus;b%29%20dx%20=%20-%5Cfrac%7B1%7D%7Ba%7Dcos%28ax@plus;b%29%20@plus;%20c" target="_blank"><img src="http://latex.codecogs.com/gif.latex?%5Cint%20sin%20%28ax+b%29%20dx%20=%20-%5Cfrac%7B1%7D%7Ba%7Dcos%28ax+b%29%20+%20c" title="\int sin (ax+b) dx = -\frac{1}{a}cos(ax+b) + c" /></a><br /><a href="http://www.codecogs.com/eqnedit.php?latex=%5Cint%20sec%5E%7B2%7D%20%28ax@plus;b%29%20dx%20=%20%5Cfrac%7B1%7D%7Ba%7Dtan%28ax@plus;b%29%20@plus;%20c" target="_blank"><img src="http://latex.codecogs.com/gif.latex?%5Cint%20sec%5E%7B2%7D%20%28ax+b%29%20dx%20=%20%5Cfrac%7B1%7D%7Ba%7Dtan%28ax+b%29%20+%20c" title="\int sec^{2} (ax+b) dx = \frac{1}{a}tan(ax+b) + c" /></a><br /><a href="http://www.codecogs.com/eqnedit.php?latex=%5Cint%20csc%5E%7B2%7D%20%28ax@plus;b%29%20dx%20=%20-%5Cfrac%7B1%7D%7Ba%7Dcot%28ax@plus;b%29%20@plus;%20c" target="_blank"><img src="http://latex.codecogs.com/gif.latex?%5Cint%20csc%5E%7B2%7D%20%28ax+b%29%20dx%20=%20-%5Cfrac%7B1%7D%7Ba%7Dcot%28ax+b%29%20+%20c" title="\int csc^{2} (ax+b) dx = -\frac{1}{a}cot(ax+b) + c" /></a><br /><a href="http://www.codecogs.com/eqnedit.php?latex=%5Cint%20sec%20%28ax@plus;b%29tan%20%28ax@plus;b%29%20dx%20=%20%5Cfrac%7B1%7D%7Ba%7Dsec%28ax@plus;b%29%20@plus;%20c" target="_blank"><img src="http://latex.codecogs.com/gif.latex?%5Cint%20sec%20%28ax+b%29tan%20%28ax+b%29%20dx%20=%20%5Cfrac%7B1%7D%7Ba%7Dsec%28ax+b%29%20+%20c" title="\int sec (ax+b)tan (ax+b) dx = \frac{1}{a}sec(ax+b) + c" /></a><br /><a href="http://www.codecogs.com/eqnedit.php?latex=%5Cint%20csc%20%28ax@plus;b%29cot%20%28ax@plus;b%29%20dx%20=%20-%5Cfrac%7B1%7D%7Ba%7Dcsc%28ax@plus;b%29%20@plus;%20c" target="_blank"><img src="http://latex.codecogs.com/gif.latex?%5Cint%20csc%20%28ax+b%29cot%20%28ax+b%29%20dx%20=%20-%5Cfrac%7B1%7D%7Ba%7Dcsc%28ax+b%29%20+%20c" title="\int csc (ax+b)cot (ax+b) dx = -\frac{1}{a}csc(ax+b) + c" /></a><br /><br />Untuk lebih jelasnya kita bisa membuktikan sebagai berikut<br />misalkan : y = ax + b<br />maka<br /><a href="http://www.codecogs.com/eqnedit.php?latex=%5Cfrac%7Bdy%7D%7Bdx%7D=a%5Crightarrow%20dx=%5Cfrac%7Bdy%7D%7Ba%7D" target="_blank"><img src="http://latex.codecogs.com/gif.latex?%5Cfrac%7Bdy%7D%7Bdx%7D=a%5Crightarrow%20dx=%5Cfrac%7Bdy%7D%7Ba%7D" title="\frac{dy}{dx}=a\rightarrow dx=\frac{dy}{a}" /></a><br />Jadi :<br /><a href="http://www.codecogs.com/eqnedit.php?latex=%5Cint%20cos%20%28ax@plus;b%29dx%20=%20%5Cint%20cos%20y%20%5Cfrac%7Bdy%7D%7Ba%7D=%5Cfrac%7B1%7D%7Ba%7D%5Cint%20cosy%20dy%20=%20%5Cfrac%7B1%7D%7Ba%7Dsiny@plus;c" target="_blank"><img src="http://latex.codecogs.com/gif.latex?%5Cint%20cos%20%28ax+b%29dx%20=%20%5Cint%20cos%20y%20%5Cfrac%7Bdy%7D%7Ba%7D=%5Cfrac%7B1%7D%7Ba%7D%5Cint%20cosy%20dy%20=%20%5Cfrac%7B1%7D%7Ba%7Dsiny+c" title="\int cos (ax+b)dx = \int cos y \frac{dy}{a}=\frac{1}{a}\int cosy dy = \frac{1}{a}siny+c" /></a><br /><a href="http://www.codecogs.com/eqnedit.php?latex==%5Cfrac%7B1%7D%7Ba%7Dsin%28ax@plus;b%29%20@plus;%20c" target="_blank"><img src="http://latex.codecogs.com/gif.latex?=%5Cfrac%7B1%7D%7Ba%7Dsin%28ax+b%29%20+%20c" title="=\frac{1}{a}sin(ax+b) + c" /></a><br /><br /><a href="http://www.codecogs.com/eqnedit.php?latex=%5Cint%20sin%20%28ax@plus;b%29dx%20=%20%5Cint%20sin%20y%20%5Cfrac%7Bdy%7D%7Ba%7D=%5Cfrac%7B1%7D%7Ba%7D%5Cint%20sin%20y%20dy%20=%20-%5Cfrac%7B1%7D%7Ba%7Dcosy@plus;c" target="_blank"><img src="http://latex.codecogs.com/gif.latex?%5Cint%20sin%20%28ax+b%29dx%20=%20%5Cint%20sin%20y%20%5Cfrac%7Bdy%7D%7Ba%7D=%5Cfrac%7B1%7D%7Ba%7D%5Cint%20sin%20y%20dy%20=%20-%5Cfrac%7B1%7D%7Ba%7Dcosy+c" title="\int sin (ax+b)dx = \int sin y \frac{dy}{a}=\frac{1}{a}\int sin y dy = -\frac{1}{a}cosy+c" /></a><br /><a href="http://www.codecogs.com/eqnedit.php?latex==%20-%5Cfrac%7B1%7D%7Ba%7Dcos%28ax@plus;b%29@plus;c" target="_blank"><img src="http://latex.codecogs.com/gif.latex?=%20-%5Cfrac%7B1%7D%7Ba%7Dcos%28ax+b%29+c" title="= -\frac{1}{a}cos(ax+b)+c" /></a><br /><br /><a href="http://www.codecogs.com/eqnedit.php?latex=%5Cint%20sec%5E%7B2%7D%20%28ax@plus;b%29dx%20=%20%5Cint%20sec%5E%7B2%7D%20y%20%5Cfrac%7Bdy%7D%7Ba%7D=%5Cfrac%7B1%7D%7Ba%7D%5Cint%20sec%5E%7B2%7D%20y%20dy%20=%20%5Cfrac%7B1%7D%7Ba%7Dtany@plus;c" target="_blank"><img src="http://latex.codecogs.com/gif.latex?%5Cint%20sec%5E%7B2%7D%20%28ax+b%29dx%20=%20%5Cint%20sec%5E%7B2%7D%20y%20%5Cfrac%7Bdy%7D%7Ba%7D=%5Cfrac%7B1%7D%7Ba%7D%5Cint%20sec%5E%7B2%7D%20y%20dy%20=%20%5Cfrac%7B1%7D%7Ba%7Dtany+c" title="\int sec^{2} (ax+b)dx = \int sec^{2} y \frac{dy}{a}=\frac{1}{a}\int sec^{2} y dy = \frac{1}{a}tany+c" /></a><br /><a href="http://www.codecogs.com/eqnedit.php?latex==%20%5Cfrac%7B1%7D%7Ba%7Dtan%28ax@plus;b%29@plus;c" target="_blank"><img src="http://latex.codecogs.com/gif.latex?=%20%5Cfrac%7B1%7D%7Ba%7Dtan%28ax+b%29+c" title="= \frac{1}{a}tan(ax+b)+c" /></a><br /><br /><a href="http://www.codecogs.com/eqnedit.php?latex=%5Cint%20csc%5E%7B2%7D%20%28ax@plus;b%29dx%20=%20%5Cint%20csc%5E%7B2%7D%20y%20%5Cfrac%7Bdy%7D%7Ba%7D=%5Cfrac%7B1%7D%7Ba%7D%5Cint%20csc%5E%7B2%7D%20y%20dy%20=%20-%5Cfrac%7B1%7D%7Ba%7Dcoty@plus;c" target="_blank"><img src="http://latex.codecogs.com/gif.latex?%5Cint%20csc%5E%7B2%7D%20%28ax+b%29dx%20=%20%5Cint%20csc%5E%7B2%7D%20y%20%5Cfrac%7Bdy%7D%7Ba%7D=%5Cfrac%7B1%7D%7Ba%7D%5Cint%20csc%5E%7B2%7D%20y%20dy%20=%20-%5Cfrac%7B1%7D%7Ba%7Dcoty+c" title="\int csc^{2} (ax+b)dx = \int csc^{2} y \frac{dy}{a}=\frac{1}{a}\int csc^{2} y dy = -\frac{1}{a}coty+c" /></a><br /><a href="http://www.codecogs.com/eqnedit.php?latex==%20-%5Cfrac%7B1%7D%7Ba%7Dcot%28ax@plus;b%29@plus;c" target="_blank"><img src="http://latex.codecogs.com/gif.latex?=%20-%5Cfrac%7B1%7D%7Ba%7Dcot%28ax+b%29+c" title="= -\frac{1}{a}cot(ax+b)+c" /></a><br /><br /><a href="http://www.codecogs.com/eqnedit.php?latex=%5Cint%20sec%20%28ax@plus;b%29tan%20%28ax@plus;b%29dx%20=%20%5Cint%20sec%20y%20tan%20y%20%5Cfrac%7Bdy%7D%7Ba%7D=%5Cfrac%7B1%7D%7Ba%7D%5Cint%20sec%20y%20tan%20y%20dy" target="_blank"><img src="http://latex.codecogs.com/gif.latex?%5Cint%20sec%20%28ax+b%29tan%20%28ax+b%29dx%20=%20%5Cint%20sec%20y%20tan%20y%20%5Cfrac%7Bdy%7D%7Ba%7D=%5Cfrac%7B1%7D%7Ba%7D%5Cint%20sec%20y%20tan%20y%20dy" title="\int sec (ax+b)tan (ax+b)dx = \int sec y tan y \frac{dy}{a}=\frac{1}{a}\int sec y tan y dy" /></a><br /><a href="http://www.codecogs.com/eqnedit.php?latex==%20%5Cfrac%7B1%7D%7Ba%7Dsec%20y@plus;c%20=%20%5Cfrac%7B1%7D%7Ba%7Dsec%28ax@plus;b%29@plus;c" target="_blank"><img src="http://latex.codecogs.com/gif.latex?=%20%5Cfrac%7B1%7D%7Ba%7Dsec%20y+c%20=%20%5Cfrac%7B1%7D%7Ba%7Dsec%28ax+b%29+c" title="= \frac{1}{a}sec y+c = \frac{1}{a}sec(ax+b)+c" /></a><br /><br /><a href="http://www.codecogs.com/eqnedit.php?latex=%5Cint%20csc%20%28ax@plus;b%29cot%20%28ax@plus;b%29dx%20=%20%5Cint%20csc%20y%20cot%20y%20%5Cfrac%7Bdy%7D%7Ba%7D=%5Cfrac%7B1%7D%7Ba%7D%5Cint%20csc%20y%20cot%20y%20dy" target="_blank"><img src="http://latex.codecogs.com/gif.latex?%5Cint%20csc%20%28ax+b%29cot%20%28ax+b%29dx%20=%20%5Cint%20csc%20y%20cot%20y%20%5Cfrac%7Bdy%7D%7Ba%7D=%5Cfrac%7B1%7D%7Ba%7D%5Cint%20csc%20y%20cot%20y%20dy" title="\int csc (ax+b)cot (ax+b)dx = \int csc y cot y \frac{dy}{a}=\frac{1}{a}\int csc y cot y dy" /></a><br /><br /><a href="http://www.codecogs.com/eqnedit.php?latex==%20-%5Cfrac%7B1%7D%7Ba%7Dcsc%20y@plus;c%20=%20-%5Cfrac%7B1%7D%7Ba%7Dcsc%28ax@plus;b%29@plus;c" target="_blank"><img src="http://latex.codecogs.com/gif.latex?=%20-%5Cfrac%7B1%7D%7Ba%7Dcsc%20y+c%20=%20-%5Cfrac%7B1%7D%7Ba%7Dcsc%28ax+b%29+c" title="= -\frac{1}{a}csc y+c = -\frac{1}{a}csc(ax+b)+c" /></a>
</div>
<span class="post-author vcard">
</span>MASKUN-WONG-PERJAhttp://www.blogger.com/profile/10525088792966143650noreply@blogger.com0tag:blogger.com,1999:blog-6779340957346272225.post-91457382154865870102011-12-09T23:20:00.001-08:002011-12-09T23:22:36.416-08:00SOAL LOGARITMA<div class="post-body entry-content" id="post-body-8921937977608612905">
Logaritma seringkali merupakan sesuatu yang kurang dipahami oleh
anak-anak SMA. Hal ini penyebabnya adalah mereka jarang melatih diri
dengan soal-soal yang setahap demi setahap (step by step). Untuk itu, di
sini saya susun soal-soal logaritma mulai dari soal-soal yang sangat
sederhana. Mudah-mudahan banyak bermanfaat bagi mereka yang mau belajar<br />
<br />
<a name='more'></a><br /><br />
1. <sup>3</sup>log 9 = ...<br />
2. <sup>2</sup>log 16 = ...<br />
3. <sup>5</sup>log 125 = ...<br />
4. <a href="http://www.codecogs.com/eqnedit.php?latex=%5E%7B7%7Dlog%20%5Cfrac%7B1%7D%7B7%7D=..." target="_blank"><img src="http://latex.codecogs.com/gif.latex?%5E%7B7%7Dlog%20%5Cfrac%7B1%7D%7B7%7D=..." title="^{7}log \frac{1}{7}=..." /></a><br />
5. <a href="http://www.codecogs.com/eqnedit.php?latex=%5E%7B6%7Dlog%20%5Cfrac%7B1%7D%7B36%7D=..." target="_blank"><img src="http://latex.codecogs.com/gif.latex?%5E%7B6%7Dlog%20%5Cfrac%7B1%7D%7B36%7D=..." title="^{6}log \frac{1}{36}=..." /></a><br />
6. <sup>5</sup>log 1 = ...<br />
7. <sup>11</sup>log 1 = ...<br />
8. log 100 = ...<br />
9. log 1000 = ...<br />
10. log 10.000 = ...<br />
11. <sup>49</sup> log 7 = ...<br />
12. <sup>8</sup> log 2 = ...<br />
13. <sup>9</sup>log 27 = ...<br />
14. <sup>32</sup>log 8 = ...<br />
15. <a href="http://www.codecogs.com/eqnedit.php?latex=%5E%7B3%7Dlog%209%5Csqrt%7B3%7D=..." target="_blank"><img src="http://latex.codecogs.com/gif.latex?%5E%7B3%7Dlog%209%5Csqrt%7B3%7D=..." title="^{3}log 9\sqrt{3}=..." /></a><br />
16. <a href="http://www.codecogs.com/eqnedit.php?latex=%5E%7B2%5Csqrt%7B2%7D%7Dlog%208%20=%20..." target="_blank"><img src="http://latex.codecogs.com/gif.latex?%5E%7B2%5Csqrt%7B2%7D%7Dlog%208%20=%20..." title="^{2\sqrt{2}}log 8 = ..." /></a><br />
17. <a href="http://www.codecogs.com/eqnedit.php?latex=%5E%7B2%5Csqrt%7B2%7D%7Dlog%2016%5Csqrt%7B2%7D%20=%20..." target="_blank"><img src="http://latex.codecogs.com/gif.latex?%5E%7B2%5Csqrt%7B2%7D%7Dlog%2016%5Csqrt%7B2%7D%20=%20..." title="^{2\sqrt{2}}log 16\sqrt{2} = ..." /></a><br />
18. <sup>5</sup>log 4 + <sup>5</sup>log 6,25 = ...<br />
19. <sup>3</sup>log 5 + <sup>3</sup>log 32,4 + <sup>3</sup>log 0,5 = ...<br />
20. <sup>7</sup>log 98 - <sup>7</sup>log 2 = ...<br />
21. <sup>6</sup>log 8 + <sup>6</sup>log 54 - log 2 = ...<br />
22. <a href="http://www.codecogs.com/eqnedit.php?latex=%5Cfrac%7B%5E%7B5%7Dlog%20343%7D%7B%5E%7B5%7Dlog7%7D=..." target="_blank"><img src="http://latex.codecogs.com/gif.latex?%5Cfrac%7B%5E%7B5%7Dlog%20343%7D%7B%5E%7B5%7Dlog7%7D=..." title="\frac{^{5}log 343}{^{5}log7}=..." /></a><br />
23.<a href="http://www.codecogs.com/eqnedit.php?latex=%5Cfrac%7B1%7D%7B%5E%7B5%7Dlog3%7D@plus;%5E%7B16,2%7Dlog3=..." target="_blank"><img src="http://latex.codecogs.com/gif.latex?%5Cfrac%7B1%7D%7B%5E%7B5%7Dlog3%7D+%5E%7B16,2%7Dlog3=..." title="\frac{1}{^{5}log3}+^{16,2}log3=..." /></a><br />
24. <a href="http://www.codecogs.com/eqnedit.php?latex=%5Cfrac%7B%5E%7B3%7Dlog5@plus;%5E%7B3%7Dlog6,4%7D%7B%5E%7B3%7Dlog2%7D=..." target="_blank"><img src="http://latex.codecogs.com/gif.latex?%5Cfrac%7B%5E%7B3%7Dlog5+%5E%7B3%7Dlog6,4%7D%7B%5E%7B3%7Dlog2%7D=..." title="\frac{^{3}log5+^{3}log6,4}{^{3}log2}=..." /></a><br />
25. <a href="http://www.codecogs.com/eqnedit.php?latex=%5Cfrac%7B%5E%7B2%7Dlog500-2%7D%7B%5E%7B2%7Dlog5%7D=..." target="_blank"><img src="http://latex.codecogs.com/gif.latex?%5Cfrac%7B%5E%7B2%7Dlog500-2%7D%7B%5E%7B2%7Dlog5%7D=..." title="\frac{^{2}log500-2}{^{2}log5}=..." /></a><br />
26. <sup>3</sup>log 16. <sup>5</sup>log 125. <sup>2</sup>log 243 = ...<br />
27. <sup>25</sup>log 2<sup>7</sup>log 81 <sup>32</sup>log 625 = ...<br />
28. <a href="http://www.codecogs.com/eqnedit.php?latex=%5Clarge%209%5E%7B.%5E%7B3%7Dlog5%7D=..." target="_blank"><img src="http://latex.codecogs.com/gif.latex?%5Clarge%209%5E%7B.%5E%7B3%7Dlog5%7D=..." title="\large 9^{.^{3}log5}=..." /></a><br />
29. <a href="http://www.codecogs.com/eqnedit.php?latex=%5Clarge%202%5E%7B.%5E%7B4%7Dlog7%7D=..." target="_blank"><img src="http://latex.codecogs.com/gif.latex?%5Clarge%202%5E%7B.%5E%7B4%7Dlog7%7D=..." title="\large 2^{.^{4}log7}=..." /></a><br />
30.<a href="http://www.codecogs.com/eqnedit.php?latex=%5Clarge%203%5E%7B.%5E%7B6%7Dlog5%7D.2%5E%7B.%5E%7B6%7Dlog5%7D=..." target="_blank"><img src="http://latex.codecogs.com/gif.latex?%5Clarge%203%5E%7B.%5E%7B6%7Dlog5%7D.2%5E%7B.%5E%7B6%7Dlog5%7D=..." title="\large 3^{.^{6}log5}.2^{.^{6}log5}=..." /></a>
</div>
<span class="post-author vcard">
</span>MASKUN-WONG-PERJAhttp://www.blogger.com/profile/10525088792966143650noreply@blogger.com0