I must solve for x for this function.
$e^x-20x=0$
I'm not sure what to do here. I've tried this so far but it makes no sense:
$$\begin{align*}
e^x&=20x\\
x\ln e&=\ln20+\ln x\\
\frac{x}{\ln20}&=\ln x
\end{align*}$$
I tried this as well but I'm not sure if this is right either:
$$\begin{align*}
e^x&=20x\\
\ln e^x&=\ln20x\\
x&=\ln20+\ln x
\end{align*}$$
I've got more confidence in the second try, although I don't know how to solve for an actual number.
The answer is a decimal.
Best Answer
This equation cannot be solved in terms of elementary functions. You can either use numeric methods like Newton's, or solve in terms of Lambert W function:
\begin{align*} e^x - 20x &= 0 \\ 20x &= e^x \\ xe^{-x} &= \frac{1}{20} \\ -x e^{-x} &= -\frac{1}{20} \\ -x &= W\left(-\frac{1}{20}\right) \\ x &= -W\left(-\frac{1}{20}\right) \end{align*}