RULES OF LOGARITHMS - Problem 3

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_inline78

Problem 3: Calculate tex2html_wrap_inline80 .

Answer: 1.41673569389

Solution 1: The problem can be worked two ways, as is, and expanded.

tex2html_wrap_inline80 can be written tex2html_wrap_inline84 . The tex2html_wrap_inline84 can be written

displaymath88


Solution 2: tex2html_wrap_inline90 can also be written

displaymath92


Check: The answers are the same. This means that tex2html_wrap_inline80 and tex2html_wrap_inline96 are equivalent.

Note: The numbers -.0686215613241, 1.48535725521, and 1.41673569389 are the exponents. Let's check the answer in terms of exponents.

displaymath98


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Author: Nancy Marcus

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