#### Answer

$x\approx 0.2524$

#### Work Step by Step

Solving $\mathrm{a}^{t}=b$ FOR $t$ ...
Take the logarithm (either natural or common) on both sides.
$\log(3^{5x})=\log 4\qquad$ ... apply $\log_{a}M^{p}=p\cdot\log_{a}M$
$5x\cdot\log 3=\log 4 \qquad$ ... divide with $(5\log 3)$
$x=\displaystyle \frac{\log 4}{5\log 3}\approx 0.252371901429$
$x\approx 0.2524$