Question 201588
{{{log(4,(32))}}} Start with the given expression.



{{{(log(10,(32)))/(log(10,(4)))}}} Use the change of base formula



Note: Remember the change of base formula is {{{log(b,(x))=log(10,(x))/log(10,(b))}}}




{{{(log(10,(2^5)))/(log(10,(8)))}}} Rewrite {{{32}}} as {{{2^5}}}



{{{(log(10,(2^5)))/(log(10,(2^2)))}}} Rewrite {{{4}}} as {{{2^2}}}



{{{(5*log(10,(2)))/(log(10,(2^2)))}}} Pull down the first exponent using the identity  {{{log(b,(x^y))=y*log(b,(x))}}}



{{{(5*log(10,(2)))/(2*log(10,(2)))}}} Pull down the second exponent using the identity  {{{log(b,(x^y))=y*log(b,(x))}}}



{{{(5*highlight(log(10,(2))))/(2*highlight(log(10,(2))))}}} Highlight the common terms.



{{{(5*cross(log(10,(2))))/(2*cross(log(10,(2))))}}} Cancel out the common terms.



{{{5/2}}} Simplify



So {{{log(4,(32))=5/2}}}