document.write( "Question 34528: Solve:
\n" ); document.write( "8^(4x-3)= 1/16, find the exact answer. \n" ); document.write( "

Algebra.Com's Answer #20827 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"8%5E%284%2Ax+-+3%29+=+1%2F16\"$
\n" ); document.write( "note that $\"x%5E%28a%2Bb%29+=+x%5Ea+%2A+x%5Eb\"$
\n" ); document.write( " $\"8%5E%284%2Ax%29+%2A+8%5E%28-3%29+=+1%2F16\"$
\n" ); document.write( "multiply both sides by 8^3
\n" ); document.write( " $\"8%5E%284%2Ax%29+=+8%5E3+%2F+16\"$
\n" ); document.write( " $\"8%5E%284%2Ax%29+=+32\"$
\n" ); document.write( "take log base 10 of both sides
\n" ); document.write( " $\"log%288%5E%284%2Ax%29%29+=+log%2832%29\"$
\n" ); document.write( "note that $\"log+x%5Ea+=+a%2Alog%28x%29\"$
\n" ); document.write( " $\"4+%2A+x+%2A+log%288%29+=+log%2832%29\"$
\n" ); document.write( " $\"x+=+log%2832%29+%2F+%284+%2A+log%288%29%29\"$
\n" ); document.write( " $\"x+=+1.50515+%2F+%284+%2A+.90309%29\"$
\n" ); document.write( " $\"x+=+1.50515+%2F+3.61236\"$
\n" ); document.write( " $\"x+=+.41667\"$
\n" ); document.write( "check this by subbing in the original equation
\n" ); document.write( "I get $\"8%5E%28-4%2F3%29+=+1%2F16\"$
\n" ); document.write( "this is true- checks
\n" ); document.write( "------------------
\n" ); document.write( "note also- $\"32+=+8%5E%285%2F3%29\"$
\n" ); document.write( " $\"8%5E%284%2Ax%29+=+8%5E%285%2F3%29\"$
\n" ); document.write( " $\"4%2Ax+=+5%2F3\"$
\n" ); document.write( " $\"x+=+5%2F12\"$
\n" ); document.write( "this is a more \"exact\" answer, since there is no rounding to a certain number
\n" ); document.write( "of decimal points
\n" ); document.write( " \n" ); document.write( "

\n" );