Question 198851
{{{(1/2)log(a,(x))+3*log(a,(y))-2*log(a,(x))}}} Start with the given expression.



{{{log(a,(x^(1/2)))+log(a,(y^3))-log(a,(x^2))}}}  Rewrite the logs using the identity  {{{y*log(b,(x))=log(b,(x^y))}}}



{{{log(a,(sqrt(x)))+log(a,(y^3))-log(a,(x^2))}}} Convert to radical notation.



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



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



So {{{(1/2)log(a,(x))+3*log(a,(y))-2*log(a,(x))=log(a,((sqrt(x)*y^3)/(x^2)))}}}