Answer
$y=\log_3{x}$
Work Step by Step
The graph contains the point $(9, 2)$.
This means that the x and y-coordinates of this point satisfy the equation $y=\log_a{x}$.
Substitute the x and y values into the given equation to obtain:
$2 = \log_a{9}$
RECALL:
$y=\log_a{x} \longrightarrow a^y=x$
Use the rule above to obtain:
$2 = \log_a{9} \longrightarrow a^2 = 9$
Note that $9=3^2$ so the expression above is equivalent to:
$a^2 = 3^2$
Use the rule $a^m = b^m \longrightarrow a =b$ to obtain:
$a=3$
Thus, the equation of the function whose graph is given is $y=\log_3{x}$.
