CHANGING THE BASE OF A LOGARITHM - Example

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.