I'm new to this and not really sure what if what I want to do is to find the inverse of an exponential but here it goes. Say I have the equation:
$\frac{Q}{A}=\exp\big(b(c-d)\big)$
How do I solve for $c$?
Is it correct to write:
$c = \frac{1}{b}\big(\log\big(\frac{Q}{A}\big)+bd\big)$
The way to reassure yourself that you have got the answer correct is to go very slowly, taking the smallest possible steps. In this case: $$\frac Q A=\exp(b(c-d))$$
Take the logarithm of both sides: $$\log\frac Q A=b(c-d)$$
Divide both sides by $b$: $$\frac 1 b \log\frac Q A=c-d$$
Add $d$ to both sides: $$\frac 1 b \log\frac Q A + d=c$$
This is the same answer as yours. Because the steps are so tiny, you can verify each of them with certainty. This may feel embarrassing because there are sure to be people who can do several steps in their heads, but being embarrassed is better than being incorrect!