document.write( "Question 1069845: Solve the following simultaneous equation
\n" ); document.write( "1) log8(xy) = 3
\n" ); document.write( "2) log2(x) * log2(y) = 18 \n" ); document.write( "

Algebra.Com's Answer #685048 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"log%288%2C%28xy%29%29=3\"$
\n" ); document.write( " $\"xy=8%5E3\"$
\n" ); document.write( " $\"xy=512\"$
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( " $\"log%282%2C%28x%29%29%2Alog%282%2C%28y%29%29=18\"$
\n" ); document.write( " $\"log%282%2C%28x%29%29%2Alog%282%2C%28512%2Fx%29%29=18\"$
\n" ); document.write( " $\"log%282%2C%28x%29%29%2A%28log%282%2C%28512%29%29-log%282%2C%28x%29%29%29=18\"$
\n" ); document.write( " $\"log%282%2C%28x%29%29%2A%289-log%282%2C%28x%29%29%29=18\"$
\n" ); document.write( "Use a substitution,
\n" ); document.write( " $\"u=log%282%2C%28x%29%29\"$
\n" ); document.write( " $\"u%289-u%29=18\"$
\n" ); document.write( " $\"-u%5E2%2B9u-18=0\"$
\n" ); document.write( " $\"u%5E2-9u%2B18=0\"$
\n" ); document.write( " $\"%28u-3%29%28u-6%29=0\"$
\n" ); document.write( "Two \"u\" solutions,
\n" ); document.write( " $\"u-3=0\"$
\n" ); document.write( " $\"u=3\"$
\n" ); document.write( "and
\n" ); document.write( " $\"u-6=0\"$
\n" ); document.write( " $\"u=6\"$
\n" ); document.write( "So,
\n" ); document.write( " $\"log%282%2C%28x%29%29=3\"$
\n" ); document.write( " $\"x=2%5E3\"$
\n" ); document.write( " $\"x=8\"$
\n" ); document.write( "and
\n" ); document.write( " $\"log%282%2C%28x%29%29=6\"$
\n" ); document.write( " $\"x=2%5E6\"$
\n" ); document.write( " $\"x=64\"$
\n" ); document.write( "So
\n" ); document.write( " $\"x=8\"$ , $\"y=512%2F8=64\"$
\n" ); document.write( "and
\n" ); document.write( " $\"x=64\"$ , $\"y=512%2F64=8\"$ \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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