Question 201587
{{{log(8,(1/16))}}} Start with the given expression.



{{{(log(10,(1/16)))/(log(10,(8)))}}} 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^(-4))))/(log(10,(8)))}}} Rewrite {{{1/16}}} as {{{2^(-4)}}}



{{{(log(10,(2^(-4))))/(log(10,(2^3)))}}} Rewrite {{{8}}} as {{{2^3}}}



{{{(-4*log(10,(2)))/(log(10,(2^3)))}}} Pull down the first exponent using the identity  {{{log(b,(x^y))=y*log(b,(x))}}}



{{{(-4*log(10,(2)))/(3*log(10,(2)))}}} Pull down the second exponent using the identity  {{{log(b,(x^y))=y*log(b,(x))}}}



{{{(-4*highlight(log(10,(2))))/(3*highlight(log(10,(2))))}}} Highlight the common terms.



{{{(-4*cross(log(10,(2))))/(3*cross(log(10,(2))))}}} Cancel out the common terms.



{{{-4/3}}} Simplify




So {{{log(8,(1/16))=-4/3}}}