Inverting the exponential decay equation?

Question

How would I algebraically isolate $x$ in the following exponential decay equation, so that $x$ is most easily derived?

$$ y = A e^{-\lambda x} \quad $$

Answer 1

Apply $\log$ on both sides :

$$\log(y) = \log(Ae^{-\lambda x}) = \log(A) + \log(e^{-\lambda x}) = \log(A) -\lambda x\log(e) = \log(A) - \lambda x.$$

Therefore (if $\lambda \neq 0$) we got $$x = \frac{\log(A) - \log(y)}{\lambda}$$