# How do you solve log_9x=2?

Nov 13, 2016

${\log}_{9} x = 2$

Use the log rule: If ${\log}_{b} x = a$, then ${b}^{a} = x$

${9}^{2} = x$

$x = 81$

Nov 13, 2016

$x = 81$

#### Explanation:

From definition of logarithm

if ${a}^{m} = b$ then ${\log}_{a} b = m$

and vice versa i.e. if ${\log}_{a} b = m$ then ${a}^{m} = b$

Hence ${\log}_{9} x = 2$ implies ${9}^{2} = x$

i.e. $x = 81$