**
Let a, b, and x be positive real numbers such that neither a nor b equals 1.
Then can be converted to the base b by the formula
.**

Let's verify this with the following example.

**Example 2:** Find .

**Answer:** 0.477962

**Solution:** You know the answer will be between 0 and 1 because

and and 5 is between 1 and 29.

Convert to the base e.

**Check:** Let's check the answer. If equals 5,
we have worked the problem correctly. =
5.000008. Close enough.

**If you would like to review another example of changing the base of a
logarithm, click on
Example.**

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