# How do you solve 3^x=log 4?

$x = - 0.4619$
If ${3}^{x} = \log 4$
then ${\log}_{3} \left(\log 4\right) = x$ or
$x = {\log}_{3} \left(\log 4\right) = \log \frac{\log 4}{\log} 3 = \log \frac{0.60206}{0.4771} = \frac{- 0.22036}{0.4771} = - 0.4619$