How do you evaluate g(x)=log_ax for x=a^2?

May 31, 2018

$g \left(x\right) = 2$

Explanation:

Inputting ${a}^{2}$ for $x$, we get

$g \left(x\right) = {\log}_{a} \left({a}^{2}\right)$

At this point, the key realization here is that we can leverage the logarithm property

${\log}_{a} \left(a\right) = 1$

${\log}_{a}$ and $a$ cancel each other out, so we essentially have

$g \left(x\right) = \cancel{{\log}_{a}} \left({\cancel{a}}^{2}\right)$

$\implies g \left(x\right) = 2$

Hope this helps!