A28­4Notes.notebook October 27, 2015 Algebra 2 Ch.8 Notes Page 48 P48 8­4 Properties of Logarithms Aug 19­6:20 AM Properties of Logarithms For any positive numbers, M, N, and b, b ≠ 0 logb MN = logb M + logb N Product Property logb M/N = logb M ­ logb N Quotient Property logb Mx = xlogb M Power Property Logs can only be combined if they have the same bases. Nov 20­7:26 AM 1 A28­4Notes.notebook October 27, 2015 Properties of Logs: Examples log52 + log56 log28 + log24 3logb4 ­ 3logb2 Nov 20­7:27 AM Simplifying and Expanding Logs Write each expression as a single logarithm. Expand each logarithm. Nov 20­7:27 AM 2 A28­4Notes.notebook October 27, 2015 HW #50 8­4 P457 #1­5,11­15,19­24,28,32 Please put your name and class period at the top of the homework. Also include the homework number. Aug 19­6:25 AM Word Problem Introduction (Do Not Copy ­ Just Read) P546 Nov 20­7:28 AM 3 A28­4Notes.notebook October 27, 2015 Example: Noise Reduction L = 10 log I / I0 L is loudness I is the intensity of the sound in watts/meter2 I0 is the lowest­Intensity sound that can be heard by an average human. An airport shipping company wants to decrease the intensity of the sound of the airplanes it uses to 25% of the current level. By how many decibels would the loudness of the sound be decreased? Let I1 = Present Intensity Let I2 = Reduced Intensity Let L1 = Present Loudness Let L2 = Reduced Loundess I2 = .25I1 L1 = 10 log I1 / I0 L2 = 10 log I2 / I0 L1 ­ L2 = Nov 20­7:28 AM 4