# How do you solve log_b(5)=0.558?

May 3, 2016

I found $b = {e}^{2.8843} = 17.89 \approx 18$

#### Explanation:

I would try changing base to your log choosing the natural log, i.e., $\ln$:

$\frac{\ln \left(5\right)}{\ln \left(b\right)} = 0.558$
so rearranging:
$\ln \left(b\right) = \frac{\ln \left(5\right)}{0.558} = 2.8843$
now we apply the definition of log to get:
$b = {e}^{2.8843} = 17.89 \approx 18$