RULES OF LOGARITHMS - Problem 1

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_inline36

Problem 1: Calculate tex2html_wrap_inline38 .

Answer: 5.63478960317

Solution: The problem can be worked two ways, as is, and expanded.

tex2html_wrap_inline38 can be written Ln280=5.63478960317 .
tex2html_wrap_inline38 can also be written

displaymath46

Since the answers are the same, then

displaymath48


Note: The numbers 1.94591014906, 3.68887945411, and 5.63478960317 are the exponents. Ln means the base is e. Let's check the answer in terms of exponents:

displaymath50


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Author: Nancy Marcus

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