document.write( "Question 239148: PLEASE HELP
\n" ); document.write( "solve for x:
\n" ); document.write( "9/2 log(base4)x=5 \n" ); document.write( "

Algebra.Com's Answer #175639 by jsmallt9(3758) $\"\"$ $\"About$

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$\"%289%2F2%29%2Alog%284%2C+%28x%29%29+=+5\"$
\n" ); document.write( "Solving logarithmic equations where the variable is in the argument of a logarithm is often done by transforming the equation into one of the following forms:
\n" ); document.write( "log(expression-with-variable) = other-expression
\n" ); document.write( "or
\n" ); document.write( "log(expression-with-variable) = log(other-expression)
\n" ); document.write( "The transformations can be done using basic Algebra and/or the properties of logarithms.

\n" ); document.write( "For your equation all we need to do to achieve one of these forms is to eliminate the 9/2. The easiest to to this is to multiply both sides of the equation by its reciprocal, 2/9:
\n" ); document.write( " $\"%282%2F9%29%289%2F2%29%2Alog%284%2C+%28x%29%29+=+%282%2F9%295\"$
\n" ); document.write( "which simplifies to
\n" ); document.write( " $\"log%284%2C+%28x%29%29+=+10%2F9\"$
\n" ); document.write( "which fits the first of the desired forms. To solve equations in this form we use the fact that $\"log%28a%2C+%28p%29%29+=+q\"$ is equivalent to $\"p+=+a%5Eq\"$ to rewrite the equation in exponential form:
\n" ); document.write( " $\"x+=+4%5E%2810%2F9%29\"$
\n" ); document.write( "Using a calculator on the right side we get:
\n" ); document.write( " $\"x+=+4.6661161583044663\"$
\n" ); document.write( "(Round this off as desired.)\r
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