## Calculus, 10th Edition (Anton)

$x=e^2$
Putting a base $e$ under each side of the equation gives $e^{ln(1/x)}=e^{-2}$, which equals $\frac{1}{x}=e^{-2}$. Rewriting the equation as $$\frac{1}{x}=\frac{1}{e^{2}}$$ allows cross multiplication to be performed. This yields $x=e^2$.