From the graph given, you can see that the curve cuts the x axis at x = 1. This means that the function of the log to base 5 will be x-1. Hence the fucntion for the graph is expressed as:
[tex]f(x)=\log _5(x-1)[/tex]
Hence option C is correct
Note that all you need to do is take the log of the function (x-1) to the base of 5
