7.1.4 Properties of Logarithms Key Objectives • Use properties to simplify logarithmic expressions. • Translate between logarithms in any base.
Notice that the x in the logarithmic equation log b a = x is the exponent in the exponential form b x = a . Because a logarithm is an exponent, the properties of exponents also apply to logarithms. Special Properties of Logs Logarithm of Base b : log b b = 1, because b 1 = b Logarithm of 1: log b 1 = 0, because b 0 = 1 Example 1 Adding Logarithms The Product Property of Logarithms can be used to write a sum of logarithms with the same base as a single logarithm.
Example 2 Subtracting Logarithms The Quotient Property of Logarithms can be used to write a difference of logarithms with the same base as a single logarithm.
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