document.write( "Question 977136: logarithem silmautanious equation.
\n" ); document.write( "log base8 (xy)=3,
\n" ); document.write( "(log base2 x)(log base2 y)=18 \n" ); document.write( "

Algebra.Com's Answer #598638 by anand429(138) $\"\"$ $\"About$

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$\"log%288%2Cxy%29=3\"$
\n" ); document.write( "=> $\"8%5E3+=+xy\"$ ----(i)
\n" ); document.write( "Also,
\n" ); document.write( " $\"log%282%2Cx%29+%2A+log+%282%2Cy%29+=18\"$
\n" ); document.write( "=> $\"log%282%2Cx%29%2Alog%282%2C512%2Fx%29=18\"$ (using (i))
\n" ); document.write( "=> $\"log%282%2Cx%29%2A%28log%282%2C512%29-log%282%2Cx%29%29=18\"$
\n" ); document.write( "=> $\"log%282%2Cx%29%2A%28log%282%2C2%5E9%29-log%282%2Cx%29%29=18\"$
\n" ); document.write( "=> $\"log%282%2Cx%29%2A%289%2Alog%282%2C2%29-log%282%2Cx%29%29=18\"$
\n" ); document.write( "=> $\"log%282%2Cx%29%2A%289%2A1-log%282%2Cx%29%29=18\"$
\n" ); document.write( "Taking $\"log%282%2Cx%29\"$ as p,
\n" ); document.write( " $\"p%2A%289-p%29=18\"$
\n" ); document.write( "=> $\"p%5E2-9p%2B18+=+0\"$
\n" ); document.write( "=> $\"%28p-3%29%28p-6%29=0\"$
\n" ); document.write( "=> $\"+p=3\"$ or $\"p=6\"$
\n" ); document.write( "So,
\n" ); document.write( " $\"log%282%2Cx%29+=+3\"$ or $\"log%282%2Cx%29+=+6\"$
\n" ); document.write( "=> $\"x=2%5E3\"$ or $\"x=2%5E6\"$
\n" ); document.write( "=> $\"x=8\"$ or $\"x=64\"$
\n" ); document.write( "=> $\"y=64\"$ or $\"y=8\"$ (Using eqn. (i))
\n" ); document.write( "So the answer sets of x and y are (8,64) or (64,8) \n" ); document.write( "

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