RULES OF LOGARITHMS

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_inline94

Logarithmic Rule 2: tex2html_wrap_inline96

Logarithmic Rule 3: tex2html_wrap_inline98

Since logarithms are nothing more than exponents, these rules come from the rules of exponents. Let a be greater than 0 and not equal to 1, and let n and m be real numbers.

Exponential Rule 1: tex2html_wrap_inline100

Example: Let a = 5, n = 2, and m = 6. tex2html_wrap_inline102 and tex2html_wrap_inline104

Exponential Rule 2: tex2html_wrap_inline106

Example: Let a = 5, n = 2, and m = 6. tex2html_wrap_inline108 and tex2html_wrap_inline110

Exponential Rule 3: tex2html_wrap_inline112

Example: Let a = 5, n = 2, and m = 6. tex2html_wrap_inline114 and tex2html_wrap_inline116

If you want to review exponential rules in detail with examples and problems, click on Exponential Rules.

If you want to review logarithmic rules in detail with examples and problems, click on one of the following rules.

Rule 1:

Rule 2:

Rule 3:

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Author: Nancy Marcus

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