document.write( "Question 1151062: Log8x+log4(1/6)=1/3 \n" ); document.write( "

Algebra.Com's Answer #772685 by greenestamps(13203) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( " $\"log%288%2Cx%29%2Blog%284%2C%281%2F6%29%29+=+1%2F3\"$

\n" ); document.write( "Convert the log base 8 and the log base 4 to logs base 2:

\n" ); document.write( " $\"%281%2F3%29log%282%2Cx%29%2B%281%2F2%29log%282%2C%281%2F6%29%29=+1%2F3\"$

\n" ); document.write( "Convert the expression on the left to a single log base 2 using rules of logarithms:

\n" ); document.write( " $\"log%282%2C%28%28x%5E%281%2F3%29%2A%281%2F6%29%5E%281%2F2%29%29%29%29+=+1%2F3\"$

\n" ); document.write( "Convert the logarithmic equation to exponential form:

\n" ); document.write( " $\"x%5E%281%2F3%29%2A%281%2Fsqrt%286%29%29+=+2%5E%281%2F3%29\"$

\n" ); document.write( "Isolate the term with the variable:

\n" ); document.write( " $\"x%5E%281%2F3%29+=+2%5E%281%2F3%29%2Asqrt%286%29\"$

\n" ); document.write( "Cube both sides of the equation:

\n" ); document.write( " $\"x+=+2%2A%286%2Asqrt%286%29%29\"$
\n" ); document.write( " $\"x+=+12%2Asqrt%286%29\"$

\n" ); document.write( " \n" ); document.write( "

\n" );