Log Rules - h1014v1

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Algebra LOGARITHMS Examples: log₂ 8 = 3 since 8 = 2³ log₁₀ 0.01 = -2 since 0.01 = 10^-2 log₅ 5 = 1 since 5 = 5¹ log_b 1 = 0 since 1 = b From the above illustration, it is evident that a logarithm is an exponent. 3⁴ is called the exponential form of the number 81. In logarithmic form, 3⁴ would be expressed as log₃ 81 = 4, or the logarithm of 81 to the base 3 is 4. Note the symbol for taking the logarithm of the number 81 to a particular base 3, is log₃ 81, where the base is indicated by a small number written to the right and slightly below the symbol log. Log Rules Since logs are exponents, the rules governing logs are very similar to the laws of exponents. The most common log rules are the following: 1. log_b (ABC) = log_b A + log_b B + log_b C 2. log_b (A/B) = log_b A - log_b B 3. log_b (Aⁿ) = nlog_b A 4. log_b b = 1 5. log_b = log_b A^1/n = (1/n)log_b A n A 6. log_b 1 = 0 7. log_b (1/A) = log_b 1 - log_b A = -log_b A Rev. 0 Page 65 MA-02

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