Answer: Option C: [tex]f\left(x\right)=\log_{5}x[/tex]
From the given graph we see the point (5, 1). It means for x = 5, f(x) = 1.
We get this only for [tex]f\left(x\right)=\log_{5}x[/tex].
We can check by plugging x = 5 in the given equation.
[tex]f\left(5\right)=\log_{5}5=1[/tex].
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