Question

What is the logarithmic function modeled by the following table?

x f(x)
5 1
25 2
125 3

Answer 1

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

Answer 2

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)