Answer
(a) $x=\frac{14\log 0.1}{\log 3}$
(b) $x\approx-29.342646$
Work Step by Step
(a) We need to solve:
$3^{x/14}=0.1$
We take the log of both sides and use log rules to simplify:
$\log 3^{\frac{x}{14}}=\log 0.1$
$(\frac{x}{14})\log 3=\log 0.1$
$\frac{x}{14}=\frac{\log 0.1}{\log 3}$
$x=\frac{14\log 0.1}{\log 3}$
(b) We solve using a calculator:
$x\approx -29.342646$
