Common and Natural Logarithms

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LOGARITHMS Algebra Example 6: Calculate log₁₀ 1. Solution: Rule 6. log_b 1 = 0 log₁₀ 1 = 0 Example 7: Calculate -log₁₀ 2. Solution: Rule 7: log_b (1/A) = -log_bA -log₁₀ 2 = log₁₀ (1/2) = -log₁₀ 0.5 = -0.3010 Common and Natural Logarithms In scientific and engineering practice, the natural system of logarithms uses the number 2.718281828459042. Since this number is frequently encountered, the letter e is used. Many natural occurrences can be expressed by exponential equations with e as the base. For example, the decay of radioactive isotopes can be expressed as a natural logarithm equation. These logarithmic expressions are called natural logs because e is the basis for many laws of nature. The expression ln is used to represent a logarithm when e is the base. Therefore, the exponential equation is written as e^x = N. and the logarithm expression is written as log_e N = x or lnN = x. As with base 10 logs (common logs), natural logs can be determined easily with the aid of a calculator. MA-02 Page 68 Rev. 0

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