# How do you solve log_9x = 1.5?

Jun 11, 2016

I found $x = 27$

#### Explanation:

We can write it trying to manipualte $1.5$ into $\frac{3}{2}$:
${\log}_{9} \left(x\right) = \frac{3}{2}$
we use the definition of log:
$x = {9}^{\frac{3}{2}}$
and the property of exponents:
$x = \sqrt{{9}^{3}}$
$x = 27$