## Calculus with Applications (10th Edition)

$$\left(e^{3}\right)^{-2 x} =e^{-x+5}$$ So, the solution of the given equation is $$x=-1.$$
$$\left(e^{3}\right)^{-2 x} =e^{-x+5}$$ Since the bases is the same, then we have \begin{aligned}\left(e^{3}\right)^{-2 x} &=e^{-x+5} \\ e^{-6 x} &=e^{-x+5} \\-6 x &=-x+5 \\-5 x &=5 \\ x &=-1 \end{aligned} So, the solution of the given equation is $$x=-1.$$