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 .
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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Author: Nancy Marcus