Question 116270
{{{log(3,(root(4,(x^5y^4)/81)))}}} Start with the given expression



{{{log(3,(((x^5y^4)/81)^(1/4)))}}} Rewrite {{{root(4,(x^5y^4)/81)}}} as {{{((x^5y^4)/81)^(1/4)}}}



{{{log(3,(((x^(5/4)y^(4/4))/81^(1/4))))}}} Distribute the exponent



{{{log(3,(((x^(5/4)y)/3)))}}} Simplify



{{{log(3,((x^(5/4)y)))-log(3,(3))}}} Break up the log using the identity {{{log(b,(x/y))=log(b,(x))-log(b,(y))}}}



{{{log(3,((x^(5/4))))+log(3,(y))-log(3,(3))}}} Break up the log using the identity {{{log(b,(x*y))=log(b,(x))+log(b,(y))}}}



{{{(5/4)log(3,(x))+log(3,(y))-log(3,(3))}}} Rewrite the first log using the identity {{{log(b,(x^y))=y*log(b,(x))}}}



{{{(5/4)log(3,(x))+log(3,(y))-1}}} Now evaluate {{{log(3,(3))}}} to get 1