CHANGING THE BASE OF A LOGARITHM - Problem 4

Let a, b, and x be positive real numbers such that neither a nor b equals 1 (remember x must be greater than 0). Then tex2html_wrap_inline52 can be converted to the base b by the formula tex2html_wrap_inline54.


Problem 4: Convert tex2html_wrap_inline56 to the base 2

Answer: tex2html_wrap_inline58 or tex2html_wrap_inline60

Solution: Convert tex2html_wrap_inline56 to the base 2.

displaymath64

The numerator can be calculated by converting the numerator to the base 10 or the base e. tex2html_wrap_inline66 . The answer tex2html_wrap_inline58 can also be written tex2html_wrap_inline60 .

Note that for this problem to be valid, the base (a + b) must be greater than zero.

If you would like to review the rules of logarithms, click on Rules.

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Author: Nancy Marcus

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