document.write( "Question 1114566: What are all the values of $\"x\"$ in which $\"log%282x%2C%2848%2Aroot%283%2C3%29%29%29=log%283x%2C+%28162+%2A+root%283%2C2%29%29%29\"$ ? \n" ); document.write( "

Algebra.Com's Answer #729522 by greenestamps(13334) $\"\"$ $\"About$

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\n" ); document.write( " $\"log%282x%2C%2848%2Aroot%283%2C3%29%29%29=n\"$ --> $\"%282x%29%5En+=+48%2Aroot%283%2C3%29\"$
\n" ); document.write( " $\"log%283x%2C+%28162+%2A+root%283%2C2%29%29%29=n\"$ --> $\"%283x%29%5En+=+162%2Aroot%283%2C2%29\"$

\n" ); document.write( "Then

\n" ); document.write( " $\"%282x%29%5En%2F%283x%29%5En+=+%2848%2Aroot%283%2C3%29%29%2F%28162%2Aroot%283%2C2%29%29\"$
\n" ); document.write( "

\n" ); document.write( " $\"%282%2F3%29%5En+=+%282%5E%288%2F3%29%29%2F%283%5E%288%2F3%29%29\"$
\n" ); document.write( " $\"n+=+8%2F3\"$

\n" ); document.write( "Then solve either of the original expressions in exponential form to solve for x:

\n" ); document.write( " $\"%282x%29%5E%288%2F3%29+=+48%2Aroot%283%2C3%29\"$
\n" ); document.write( " $\"%282%29%5E%288%2F3%29%28x%29%5E%288%2F3%29+=+%282%5E4%29%283%5E%284%2F3%29%29\"$
\n" ); document.write( " $\"x%5E%288%2F3%29+=+%282%5E%284%2F3%29%29%283%5E%284%2F3%29%29+=+6%5E%284%2F3%29\"$
\n" ); document.write( " $\"x+=+sqrt%286%29\"$

\n" ); document.write( "Answer: There is one value -- $\"x=sqrt%286%29\"$ -- that satisfies the given equation. \n" ); document.write( "

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