# How do you evaluate log_9 x=3/2?

Oct 27, 2016

$x = 27$

#### Explanation:

Remember that in general ${\log}_{b} a = c$ means ${b}^{c} = a$
(You really need to memorize this; it's a basic definition.)

Therefore ${\log}_{9} x = \frac{3}{2}$
means
$\textcolor{w h i t e}{\text{XXX}} {9}^{\frac{3}{2}} = x$

$\rightarrow \textcolor{w h i t e}{\text{XX}} x = {9}^{\frac{3}{2}}$

$\textcolor{w h i t e}{\text{XXXX}} = {\left({9}^{\frac{1}{2}}\right)}^{3}$

$\textcolor{w h i t e}{\text{XXXX}} = {\left(+ 3\right)}^{3}$ (the negative root can be ignored since log arguments must be positive)

$\textcolor{w h i t e}{\text{XXXX}} = 27$