What is the logarithmic function modeled by the following table?

x f (x)

5 1

25 2

125 3

So we need to come up with a function that when we plug x into it, it gives us f (x). Logarithims ask: what exponent do I need to put on b (see the diagram to see what b is) to make it equal x. In the diagram below y is our f (x).

So we have logb (x) = f (x), we need to find what b is. Well the values look like 5 then 5 squared, then 5 cubed etc. So b=5.

To test this put one of the exponents (f (x) - values) on b and see if it equals the x value next to it in the table.

The answer is:

log 5 x = f (x)

The answer would be the following: f (x) = 5^x