document.write( "Question 970068: Solve for x. ((1/3)ln e^(3x)-3e^(ln x)=12. The answer is no solution but I'm not sure how to prove that it has no solution. Please help. Thank you. \n" ); document.write( "

Algebra.Com's Answer #592751 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"ln%28x%29\"$ and $\"e%5E%28x%29\"$ are inverse functions.
\n" ); document.write( " $\"ln%28e%5Ex%29=x\"$
\n" ); document.write( " $\"e%5E%28ln%28x%29%29=x\"$
\n" ); document.write( "So,
\n" ); document.write( " $\"%281%2F3%29%283x%29-3x=12\"$
\n" ); document.write( " $\"x-3x=12\"$
\n" ); document.write( " $\"-2x=12\"$
\n" ); document.write( " $\"x=-6\"$
\n" ); document.write( "However $\"x=-6\"$ is not allowed since $\"ln%28-6%29\"$ is not defined.
\n" ); document.write( "There is no solution.\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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