Given:
The function is
[tex]f(x)=\log_5(x)[/tex]
To find:
The graph of the given function.
Solution:
We have,
[tex]f(x)=\log_5(x)[/tex]
At x=1,
[tex]f(1)=\log_5(1)[/tex]
[tex]f(1)=0[/tex] [tex][\because \log_a(1)=0, a>0][/tex]At x=5,
[tex]f(5)=\log_5(5)[/tex]
[tex]f(5)=1[/tex] [tex][\because \log_aa=1][/tex]
So, the graph of given function passes through the points (1,0) and (5,1). Only graph in option A passes through these two points.
Therefore, the correct option is A.