Answer
(a) $x=\frac{\ln 19-1}{4}$
(b) $x\approx 0.486110$
Work Step by Step
(a) We need to solve:
$1+e^{4x+1}=20$
$e^{4x+1}=20-1=19$
We take the natural log of both sides and use log rules to simplify:
$\ln e^{4x+1}=\ln 19$
$4x+1=\ln 19$
$x=\frac{\ln 19-1}{4}$
(b) We solve using a calculator:
$x\approx 0.486110$
