Answer
(a) $ x\approx -2.81467$
(b) $x\approx 0.15651$
Work Step by Step
(a) Since
\begin{align*}
2^{1-3 x}&=99\\
\ln 2^{1-3 x}&=\ln (99)\\
(1-3x)\ln 2 &=\ln(99)\\
1-3x&=\frac{\ln 99}{\ln 2}\\
x&=\frac{1}{3}\left[ 1-\frac{\ln 99}{\ln 2}\right]\\
\end{align*}
Then
$$ x\approx-1.87645$$
(b) Since
\begin{align*}
\ln \left(\frac{x+1}{x}\right)&=2\\
1+\frac{1}{x} & =e^2\\
\frac{1}{x} & =e^2-1\\
x&=\frac{1}{e^2-1}
\end{align*}
then $$x\approx 0.15651$$
