Answer
$y=\log_5{x}$
Work Step by Step
The graph contains the point $(5, 1)$.
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:
$y = \log_a{x}
\\1 = \log_a{5}$
RECALL:
$y=\log_a{x} \longrightarrow a^y=x$
Use the rule above to obtain:
$1 = \log_a{5} \longrightarrow a^1 = 5$
Use the rule $a^1 = b^1 \longrightarrow a = b$ to obtain:
$a^1=5^1
\\a=5$
Thus, the equation of the function whose graph is given is $y=\log_5{x}$.
