Answer
(a) $x=\frac{1}{4}(1-\ln 2)$
(b) $x\approx 0.076713$
Work Step by Step
(a) We need to solve:
$e^{1-4x}=2 $
We take the natural log of both sides and use log rules to simplify:
$1-4x \ln e=\ln 2$
$1-4x=\ln 2$
$-4x=-1+\ln 2$
$x=\frac{1}{4}(1-\ln 2)$
(b) We use a calculator to solve:
$x\approx 0.076713$