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Logarithms By: Lulu Huang, Alison Li,Gladi Pang Period 4

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8-4 Properties of Logarithms Product Property: log b XY = log b X + log b Y Quotient Property : log b X = log b X - log b Y Y Power property: log b X y = ylogbX

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8-4 Identifying Properties Example 1: log5 + log6 = log 30 product property Example 2: log log log 5 4 = log 5 25 product and quotient property

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8-4 Simplifying Logarithms Example 1: log log 4 32 = log 4 (4 x 32) = log Example 2: log 7 X + log 7 Y - log 7 Z = log 7 (X x Y) Z = log 7 XY Z

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8-4 Expanding Logarithms Example 1: log 5 XY = log 5 X + log 5 Y Example 2: log3m4n -2 = log3 + logm4 +logn -2 = log3 + 4logm + -2logn

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8-5 Solving Exponential Equation Example 1: 7 2X = 25 log7 2X = log25 2Xlog7 = log25 log7 log 7 2X = X = Example 2: 20 2X+1 = 260 log20 2X+1 = log260 2X+1log20 = log260 log 20 log 20 2X+1 = X = X =

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8-5 Using Change Of Base Formula Change Of Base Formula: log a N = log N log a Example 1: log 3 33 = log33 log 3 Example 2: log = log135 log5

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8-5 Solving Exponential Equations by Changing Base Example 1: 2X = 5 log 2 2 X = log 2 5 Xlog 2 2 = log 2 5 Xlog2 = log5 log2 log2 X = Example 2: 7 3X+4 = 79 log 7 7 3X+4 = log X + 4 log7 = log79 log7 log7 3X + 4 = X = x =

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8-5 Solving a Logarithmic Equations 2 X2X2 = 100 2

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8-5 Using Logarithmic Properties to Solve Equation

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8-6 Simplifying Natural Logarithms Example 1: 3 ln 5 ln 5 3 = ln125 = 4.83 Example 2: ln a - 2 ln b + 2 ln c = ln a - ln b 2 + ln c 2 = ln a x c 2 b 2 = ln ac 2 b 2

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8-6 Solving Natural Logarithmic Equations

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8-6 Solving Exponential Equations

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