# Chapter 4 - Section 4.3 - Logarithmic Functions - 4.3 Exercises: 53

$y=\log_5{x}$

#### 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 $y=\log_5{x}$.

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