RULES OF LOGARITHMS - Example

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_inline50

Example 4: Suppose that a base is 4 and exponents are a, b, and c. We could simplify the exponential problem tex2html_wrap_inline52 by combing the exponents and writing the problem as tex2html_wrap_inline54 .

The same is true of logarithms. Suppose you wanted to simplify the expression tex2html_wrap_inline56 . You could so by writing tex2html_wrap_inline56 as tex2html_wrap_inline60 , providing x > 0, y>0, and Z>0..

Note: The two expressions tex2html_wrap_inline56 and tex2html_wrap_inline60 are equivalent expressions. Recall that equivalent expressions do not look the same but will result in the same answer is you substitute a value for x, for y, and for z in both expressions. Let's try it. Suppose x = 10, y = 15, and z = 20. Then

displaymath72

and

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

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Author: Nancy Marcus

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