# How do you evaluate log_8 4?

May 10, 2015

Consider that:
${\log}_{a} \left(b\right) = x \to {a}^{x} = b$
${\log}_{8} \left(4\right) = x$
${8}^{x} = 4$ that can be written as:
${\left({2}^{3}\right)}^{x} = {2}^{2}$
${2}^{3 x} = {2}^{2}$
$3 x = 2$
and $x = \frac{2}{3}$