How do you solve \log _ { 3} 9^ { x } = 10?

Oct 15, 2017

$x = 5$

Explanation:

Using the rule ${\log}_{a} M = N \Rightarrow M = {a}^{N}$ you can rewrite the equation as ${9}^{x} = {3}^{10}$

${9}^{x} = 59 049$
Log both sides to bring $x$ down so you can solve for it.
$\log {9}^{x} = \log 59049$
$x = \log \frac{59049}{\log} 9$
$x = 5$

Oct 15, 2017

The answer is $5$. See explanation.

${\log}_{3} {9}^{x} = 10$

First I use the rule:

${\log}_{a} {b}^{c} = c \cdot {\log}_{a} b$

After using this rule I get:

$x \cdot {\log}_{3} 9 = 10$

${\log}_{3} 9 = 2$, so we get: