Question 150412
{{{log(a,(x^3y^2z))}}} Start with the given expression.



{{{log(a,(x^3))+log(a,(y^2z))}}} Break up the log {{{log(a,(x^3y^2z))}}}  using the identity  {{{log(b,(A*B))=log(b,(A))*log(b,(B))}}}




{{{log(a,(x^3))+log(a,(y^2))+log(a,(z))}}} Break up the log {{{log(a,(y^2z))}}}  using the identity  {{{log(b,(A*B))=log(b,(A))*log(b,(B))}}}



{{{3*log(a,(x))+log(a,(y^2))+log(a,(z))}}} Rewrite {{{log(a,(x^3))}}} as {{{3*log(a,(x))}}} using the identity  {{{log(b,(x^y))=y*log(b,(x))}}}



{{{3*log(a,(x))+2*log(a,(y))+log(a,(z))}}} Rewrite {{{log(a,(y^2))}}} as {{{2*log(a,(y))}}} using the identity  {{{log(b,(x^y))=y*log(b,(x))}}}



So {{{log(a,(x^3y^2z))}}} expands to {{{3*log(a,(x))+2*log(a,(y))+log(a,(z))}}}