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N 11-2 Laws of Logarithms: Expanding and Condensing Log Expressions Let b be the base of a logarithmic function (b 0, b 1) . Let M and N be positive numbers or variables. 1. logb MN = logbM + logbN 2. logb M logb M logb N N 3. logbMk = k•logbM Product Property NOTE: The BASE stays the same when using these laws. Any change of base requires the use of the “change of base” formula. Quotient Property Power Property Use the laws of logarithms to expand the following expressions. 1. log2 5ab = 2. log5 8 = x 3. log2 6 x 2 y 3 = 4a2 4. log3 = bc 2 N 11-2 a5 5. log = b (NOTE: What power does a square root radical represent?) Use the laws of logarithms to condense the following expressions. 6. log57 + 3 log5x = 7. log2x – log23 = 8. 1 log6M – 3log6N = 2 9. 3 (log2a – log2b) = 10. log34 + 3log3M – 2 log3N =