document.write( "Question 607251: Solve the equation for x. ROUND your answer to TWO DECIMAL places, and do not include \"x=\" in your answer..\r
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\n" ); document.write( "\n" ); document.write( "5+8*ln x=25.8 \n" ); document.write( "

Algebra.Com's Answer #382531 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"5%2B8%2Aln%28x%29=25.8\"$
\n" ); document.write( "Solving equations where the variable is in the argument (or base) of a logarithm usually starts by using algebra and/or log properties to transform the equation into one of the following forms:
\n" ); document.write( "log(expression) = other-expression
\n" ); document.write( "or
\n" ); document.write( "log(expression) = log(other-expression)

\n" ); document.write( "Your equation, with its single logarithm, should be transformed into the first form. This can be done quite simply. Subtract 5 from each side:
\n" ); document.write( " $\"8%2Aln%28x%29+=+23.8\"$
\n" ); document.write( "Then we divide both sides by 8:
\n" ); document.write( " $\"ln%28x%29+=+23.8%2F8\"$
\n" ); document.write( "which simplifies to
\n" ); document.write( " $\"ln%28x%29+=+2.975\"$

\n" ); document.write( "The next step. with the first form, is to rewrite the equation in exponential form. In general, $\"log%28a%2C+%28p%29%29+=+q\"$ is equivalent to $\"a%5Eq+=+p\"$ . Using this pattern, and the fact that the base of ln is e, we get:
\n" ); document.write( " $\"e%5E2.975+=+x\"$

\n" ); document.write( "The next step is to solve for the variable. Your equation is already solved for the variable! All that is left, since a rounded decimal was requested, is to use your calculator:
\n" ); document.write( " $\"x+=+e%5E2.975+=+%282.71828183%29%5E2.975+=+19.59\"$ \n" ); document.write( "

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