document.write( "Question 411335: 9/4 log2(x)=3 \n" ); document.write( "

Algebra.Com's Answer #289433 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"%289%2F4%29log%282%2C+%28x%29%29=3\"$
\n" ); document.write( "First, let's isolate the logarithm. Multiplying both sides by 4/9 we get:
\n" ); document.write( " $\"%284%2F9%29%289%2F4%29log%282%2C+%28x%29%29=%284%2F9%293\"$
\n" ); document.write( "which simplifies to:
\n" ); document.write( " $\"log%282%2C+%28x%29%29=4%2F3\"$
\n" ); document.write( "With the log isloated we next rewrite the equation in exponential form. In general $\"log%28a%2C+%28p%29%29+=+q\"$ is equivalent to $\"p+=+a%5Eq\"$ . Using this pattern on your equation we get:
\n" ); document.write( " $\"x+=+2%5E%284%2F3%29\"$
\n" ); document.write( "This may be an acceptable answer. However, a preferred form might be to rewrite this in radical form:
\n" ); document.write( " $\"x+=+root%283%2C+2%5E4%29\"$
\n" ); document.write( "which can be simplified:
\n" ); document.write( " $\"x+=+root%283%2C+2%5E3%2A2%29\"$
\n" ); document.write( " $\"x+=+root%283%2C+2%5E3%29%2Aroot%283%2C+2%29\"$
\n" ); document.write( " $\"x+=+2%2Aroot%283%2C+2%29\"$ \n" ); document.write( "

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