# How do you solve 3.5^x=47.9?

Apply ${\log}_{3.5}$ on both sides. You'll get:
${\log}_{3.5} {3.5}^{x} = {\log}_{3.5} 47.9$
$x = {\log}_{3.5} 47.9$
To solve this you can change base to use natural logs, $\ln$, as:
$x = \frac{\ln \left(47.9\right)}{\ln \left(3.5\right)} = 3.088$