Let a be a positive number such that a does not equal 1, let n be a real number, and let u and v be positive real numbers.

Logarithmic Rule 1: tex2html_wrap_inline157

Example 3: Suppose that a base is 4 and exponents are 5, 2, and 3. We could solve the exponential problem tex2html_wrap_inline159 by calculating tex2html_wrap_inline161 ,

tex2html_wrap_inline163 , and tex2html_wrap_inline165 separately and multiplying the results. tex2html_wrap_inline167 , tex2html_wrap_inline169 and tex2html_wrap_inline171 and their product is tex2html_wrap_inline173 . You could also solve the problem by first combing the exponents


The same is true of logarithms. Suppose you wanted to calculate

tex2html_wrap_inline177 . You could calculate the answer by first multiplying tex2html_wrap_inline179 , changing the base of 4 to either 10 or e and calculating the results.


Or you could combine the logarithms using Rule 1 and then change the bases.


If you would like to review another example, click on Example.

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Author: Nancy Marcus

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