Rearranging An Equation To Solve?Can't?

Question

How would I rearrange the equation:

$$a=b^{(c/d)}$$

to find c?

Answer 1

Notice

$$ a = b^{c/d} \iff \log a = \frac{c}{d} \log b \iff c =\frac{d \log a}{\log b}$$

provided $b \neq 1 $ otherwise we would have $\log b = 0 $ which is not allowed. and $b > 0 $. similarly, $a > 0$ and $ d \neq 0 $