Question 169152
{{{5*log(e,(x))+log(e,(y))-2*log(e,(z))}}} Start with the given expression



{{{log(e,(x^5))+log(e,(y))-log(e,(z^2))}}} Rewrite the expression using the identity  {{{y*log(b,(x))=log(b,(x^y))}}}. In other words, place the coefficients as exponents.



{{{log(e,(x^5y))-log(e,(z^2))}}} Combine the first two logs using the identity {{{log(b,(A))+log(b,(B))=log(b,(A*B))}}}



{{{log(e,((x^5y)/(z^2)))}}} Combine the logs using the identity {{{log(b,(A))-log(b,(B))=log(b,(A/B))}}}



So {{{5*log(e,(x))+log(e,(y))-2*log(e,(z))}}} simplifies to {{{log(e,((x^5y)/(z^2)))}}}