Question 198957
{{{-4*log(4,(A))+3*log(4,(B))+3*log(4,(C))}}} Start with the given expression.



{{{-log(4,(A^4))+log(4,(B^3))+log(4,(C^3))}}} Rewrite the logs using the identity  {{{y*log(b,(x))=log(b,(x^y))}}}



{{{log(4,(B^3))+log(4,(C^3))-log(4,(A^4))}}} Rearrange the terms.



{{{log(4,(B^3*C^3))-log(4,(A^4))}}} Combine the logs using the identity {{{log(b,(A))+log(b,(B))=log(b,(A*B))}}}



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



So {{{-4*log(4,(A))+3*log(4,(B))+3*log(4,(C))=log(4,((B^3*C^3)/(A^4)))}}}