How can I solve this equation: $e^{2x^3 - 6x^2 + 3} = 0$

Question

I don't remember what I supposed to do in this situation...I know that it's necessary transform both sides of the equation in the same base. However, what I need to do when i have a 0?

My equation: $e^{2x^3 - 6x^2 + 3} = 0$

Answer 1

We have to know that $e^{\mathrm{something}}$ is never zero, so that doesn't have any solution. It is never negative, also. But, if you had $$e^{\mathrm{something}} = c > 0$$ we can take $\ln$ on both sides and get: $$\begin{align}\ln e^{\mathrm{something}} &= \ln c \\ \mathrm{something} &= \ln c\end{align}$$ That last equation you should be able to solve, normally. Don't be afraid of $\ln c$, it is just a number. Ok?