Answer
$x=\dfrac{3-\ln16}{5}\approx0.045482$
Work Step by Step
$e^{3-5x}=16$
Apply $\ln$ to both sides of the equation:
$\ln e^{3-5x}=\ln16$
The exponent $3-5x$ can be taken down to multiply in front of its respective $\ln$:
$(3-5x)\ln e=\ln16$
Since $\ln e=1$, the equation becomes:
$3-5x=\ln16$
Solve for $x$:
$-5x=\ln16-3$
$x=-\dfrac{\ln16-3}{5}=\dfrac{3-\ln16}{5}\approx0.045482$