Answer
$x=\dfrac{\ln8}{0.4}\approx5.198604$
Work Step by Step
$e^{0.4x}=8$
Apply $\ln$ to both sides of the equation:
$\ln e^{0.4x}=\ln8$
The exponent $0.4x$ can be taken down to multiply in front of the $\ln$:
$0.4x\ln e=\ln8$
Since $\ln e=1$, the equation becomes:
$0.4x=\ln8$
Solve for $x$:
$x=\dfrac{\ln8}{0.4}\approx5.198604$
