document.write( "Question 389942: if log a=2 and log b=3, what is the numerical value of
\n" ); document.write( "log square root a / b^3 ? \n" ); document.write( "

Algebra.Com's Answer #276932 by jsmallt9(3758) $\"\"$ $\"About$

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$\"log%28%28sqrt%28a%29%2Fb%5E3%29%29\"$
\n" ); document.write( "Since you're given log(a) and log(b), this expression can be evaluated if we can rewrite this expression in terms of log(a) and/or log(b). To do this we start by using the property of logarithms, $\"log%28z%2C+%28p%2Fq%29%29+=+log%28x%2C+%28p%29%29+-+log%28x%2C+%28q%29%29\"$ , to write the logarithm of a quotient as the difference of the logarithms of the numerator and denominator:
\n" ); document.write( " $\"log%28%28sqrt%28a%29%29%29+-+log%28%28b%5E3%29%29\"$
\n" ); document.write( "Since square roots are the same as an exponent of 1/2 this can be written as:
\n" ); document.write( " $\"log%28%28a%5E%281%2F2%29%29%29+-+log%28%28b%5E3%29%29\"$
\n" ); document.write( "Next we can use another property of logarithms, $\"log%28x%2C+%28p%5Eq%29%29+=+q%2Alog%28x%2C+%28p%29%29\"$ , to move the exponents in the arguments out in front:
\n" ); document.write( " $\"%281%2F2%29log%28%28a%29%29+-+3log%28%28b%29%29\"$
\n" ); document.write( "We now have the expression in terms of log(a) and log(b). We can substitute in their values:
\n" ); document.write( " $\"%281%2F2%29%282%29+-+3%283%29\"$
\n" ); document.write( "which simplifies as follows:
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