Answer
(a) $x=-\frac{1}{5}(\ln 16-3)$
(b) $x\approx 0.045482$
Work Step by Step
(a) We need to solve:
$e^{3-5x}=16$
We take the natural log of both sides and use log rules to simplify:
$3-5x \ln e=\ln 16$
$3-5x=\ln 16$
$-5x=\ln 16-3$
$x=-\frac{1}{5}(\ln 16-3)$
(b) We use a calculator to solve:
$x\approx 0.045482$
