# How do you evaluate the expression log_9 243?

Nov 4, 2016

${\log}_{9} 243 = \frac{5}{2}$

#### Explanation:

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

$y = {\log}_{9} 243 \implies {9}^{y} = 243$

recognising that $243$ is a power of $3$

${3}^{5} = 243$

and ${9}^{\frac{1}{2}} = 3$

we have${\left({9}^{\frac{1}{2}}\right)}^{5} = 243$

$\therefore {9}^{\frac{5}{2}} = 243$

$y = \frac{5}{2}$