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Section 4-3 Math 150 Lecture Notes Laws of Logarithms Laws of Logarithms Let a be a positive number, with a ≠ 1. Let A, B, and C be any real numbers with A > 0 and B > 0. 1. loga (AB) = logaA + loga B A 2. loga = loga A – loga B B 3. loga (AC) = C loga A Change of Base Formula log a x log b x = log a b Example 1: Evaluate the expression. log3 100 – log3 18 – log3 50 Example 2: Use the Laws of Logarithms to expand the expression: Example 3: Use the Laws of Logarithms to expand the expression: 1 a2 log 4 b c ln 3x 2 ( x + 1)10 Section 4-3 Example 4: Use the Laws of Logarithms to combine (condense) the expression: log5 (x2 – 1) – log5 (x – 1) Example 5: Use the Laws of Logarithms to combine (condense) the expression: 1 1 log(2 x + 1) + [log( x − 4) − log( x 4 − x 2 − 1)] 3 2 Example 6: Use the Change of Base Formula and a calculator to evaluate the logarithm, correct to four decimal places. log6 92 2