Answer
(a) $x=-\ln 11.5$
(b) $x\approx -2.442347$
Work Step by Step
(a) We need to solve:
$\frac{50}{1+e^{-x}}=4$
$50=4(1+e^{-x})$
$50=4+4e^{-x}$
$46=4e^{-x}$
$\frac{46}{4}=11.5=e^{-x}$
We take the log of both sides and use log rules to simplify:
$\ln 11.5=\ln e^{-x}$
$\ln 11.5=-x$
$x=-\ln 11.5$
(b) We solve using a calculator:
$x\approx -2.442347$