# How do you use the Change of Base Formula and a calculator to evaluate log_sqrt{5} (8)?

Jul 5, 2015

I found: ${\log}_{\sqrt{5}} \left(8\right) = \frac{\ln \left(8\right)}{\ln \left(\sqrt{5}\right)} = 2.584$

#### Explanation:

Your calculator can evaluate, for example, natural logarithms, indicated as $\ln$.
${\log}_{\sqrt{5}} \left(8\right) = \frac{\ln \left(8\right)}{\ln \left(\sqrt{5}\right)} = 2.584$

Remembering the Change of Base Formula :
${\log}_{a} \left(x\right) = {\log}_{b} \frac{x}{\log} _ b \left(a\right)$