# How do you solve log_b(3) = .234?

Apr 18, 2016

$b \approx 109.39$

#### Explanation:

If ${\log}_{b} \left(3\right) = .234$
then (by definition of $\log$
$\textcolor{w h i t e}{\text{XXX}} {b}^{.234} = 3$

$\textcolor{w h i t e}{\text{XXX}} {\left({b}^{.234}\right)}^{\frac{1}{.234}} = {3}^{\frac{1}{.234}}$

$\textcolor{w h i t e}{\text{XXX}} b = {3}^{\frac{1}{.234}} \approx {3}^{4.2735} \approx 109.3905$