How can I solve a/b by removing log?

Question

I have the below equation and need to simply find $ \frac{a}{b} $, but I am unsure how to get the logs over to the left side of the equation. Is it possible?

$0.5 = \frac{\log(a)}{\log(b)}$

I understand that $ \frac{\log(a)}{\log(b)} = \log_b(a) $, but I don't know if that will help me.

Answer 1

$log \, a=\log (b^{0.5})$ so $a =b^{0.5}$. $\frac a b$ cannot be determined uniquely from the given equation.

Answer 2

Multiplying both sides by $\log(b)$ gives $0.5\log(b)=\log(a)$, and that means $\log(b^{0.5})=\log(a)$ and $b^{0.5}=a$ or $b=a^2$.

Then, $\displaystyle \frac{a}{b}=\frac{a}{a^2}=\frac{1}{a}$, so this quantity still depends on $a$.