Answer
$x=5ln{\frac{7}{5}}$.
Work Step by Step
We know that by definition if $y=a^x$, then $log_a {y}=x$ , also $log_e {x}=ln {x}$, hence if $y=e^x$, then $ln{e^x}=log_e {e^x}=x$ and vice versa and that $ln{\frac{1}{x}}=-ln{x}$.
Hence if $5e^{0.2x}=8$, then $e^{0.2x}=\frac{7}{5}$. Thus by taking the natural logarithm of both sides we get $0.2x=ln{\frac{7}{5}}$, hence $x=5ln{\frac{7}{5}}$.
