Let a, b, and x be positive real numbers such that neither a nor b equals 1. Then tex2html_wrap_inline41 can be converted to the base b by the formula tex2html_wrap_inline43 .

Let's verify this with the following example.

Example 2: Find tex2html_wrap_inline45 .

Answer: 0.477962

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

tex2html_wrap_inline47 and tex2html_wrap_inline49 and 5 is between 1 and 29.

Convert tex2html_wrap_inline45 to the base e.


Check: Let's check the answer. If tex2html_wrap_inline55 equals 5, we have worked the problem correctly. tex2html_wrap_inline55 = 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

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