Change of base (proven)

In an earlier section on properties of logarithms, we stated two change of base formulas

and

With the calculator you can use these formulas to compute logs in bases not included on your calculator. In this section we will go over the proof of the first of these formulas. The proof of the second one is similar to the one given below.

Recall that by definition, if and only if

If we take the natural log of both sides of we have

Using property 3, we get

Solving for y we get

Since , we obtain