Answer
(a) $x=\frac{\ln 45}{\ln 3}-1$
(b) $x\approx 2.464974$
Work Step by Step
(a) We need to solve:
$2(5+3^{x+1})=100$
$5+3^{x+1}=\frac{100}{2}=50$
$3^{x+1}=50-5=45$
We take the log of both sides and use log rules to simplify (we choose the natural log, but any other base would work as well):
$\ln 3^{x+1}=\ln 45$
$(x+1) \ln3 = \ln 45$
$x+1=\frac{\ln 45}{\ln 3}$
$x=\frac{\ln 45}{\ln 3}-1$
(b) We solve using a calculator:
$x\approx 2.464974$
