Question 164881
{{{log(3,(x))-4log(3,(3y))}}} Start with the given expression



{{{log(3,(x))-log(3,((3y)^4))}}} Rewrite the second logarithm using the identity {{{y*log(b,(x))=log(b,(x^y))}}}



{{{log(3,((x)/(3y)^4))}}} Combine the logs using the identity {{{log(b,(A))-log(b,(B))=log(b,(A/B))}}}



{{{log(3,((x)/(81y^4)))}}} Expand and simplify



So {{{log(3,(x))-4log(3,(3y))}}} simplifies to {{{log(3,((x)/(81y^4)))}}}