Question 236461
{{{log(((x^2*sqrt(y))/z^3))}}} Start with the given expression.



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



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



{{{log((x^2))+log((y^(1/2)))-log((z^3))}}} Convert to rational exponent notation.



{{{2log((x))+(1/2)log((y))-3log((z))}}} Pull down the exponents using the identity  {{{log(b,(x^y))=y*log(b,(x))}}}



{{{2a+(1/2)b-3c}}} Now use the equations {{{a=log((x))}}}, {{{b=log((y))}}}, and {{{c=log((z))}}}



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