Question

If $\log_{b/a} a^2 b = 2$, where $a$ and $b$ are positive real numbers, then find $\log_{ab} b$.

Answer 1

We can rewrite $\log_{b/a} a^2 b = 2$ as $(b/a)^2a^2b=(b/a)^2\cdot ab = b^2$. Therefore, $\log_ab^2 = \boxed{2}$.