Question 201176
{{{2*log(b,(x))-3(log(b,(y))+log(b,(z)))}}} Start with the given expression.



{{{2*log(b,(x))-3*log(b,(y))-3*log(b,(z))}}} Distribute



{{{log(b,(x^2))-log(b,(y^3))-log(b,(z^3))}}} Rewrite the logs using the identity  {{{y*log(b,(x))=log(b,(x^y))}}}



{{{log(b,(x^2))-(log(b,(y^3))+log(b,(z^3)))}}} Factor out a negative from the last two terms.



{{{log(b,(x^2))-log(b,(y^3z^3))}}} Combine the last two logs using the identity {{{log(b,(A))+log(b,(B))=log(b,(A*B))}}}



{{{log(b,((x^2)/(y^3z^3)))}}} Combine the logs using the identity {{{log(b,(A))-log(b,(B))=log(b,(A/B))}}}



So {{{2*log(b,(x))-3(log(b,(y))+log(b,(z)))=log(b,((x^2)/(y^3z^3)))}}}