# How do you calculate log_8 7.9 with a calculator?

Sep 6, 2016

${\log}_{8} 7.9 = 0.9939$

#### Explanation:

Let ${\log}_{b} a = x$. Hence ${b}^{x} = a$ and log (to the base $10$) on both sides, we get

$x \log b = \log a$ or $x = \log \frac{a}{\log} b$

Hence ${\log}_{b} a = \log \frac{a}{\log} b$ and

${\log}_{8} 7.9 = \log \frac{7.9}{\log} 8$

= $\frac{0.8976}{0.9031}$

= $0.9939$