Answer
(a) $x=\frac{1-\ln 12}{4}$
(b) $x\approx -0.371227$
Work Step by Step
(a) We need to solve:
$8+e^{1-4x}=20$
$e^{1-4x}=20-8=12$
We take the log of both sides and use log rules to simplify:
$\ln e^{1-4x}=\ln 12$
$1-4x=\ln 12$
$x=\frac{1-\ln 12}{4}$
(b) We solve using a calculator:
$x\approx -0.371227$
