Warm-up 1. Convert the following log & exponential equations 1. Convert the following log & exponential equations Log equationExponential Equation Log equationExponential Equation Log 2 16 = 4? Log 2 16 = 4? Log 3 1= 0? Log 3 1= 0? ?5 2 = 25 ?5 2 = Solve these log expressions: 2. Solve these log expressions: Log 2 64log 9 9log 3 (1/9) Log 2 64log 9 9log 3 (1/9) 3. Graph this function: f(x) = log 3 (x – 2) 3. Graph this function: f(x) = log 3 (x – 2)

Warm-up 1. Convert the following log & exponential equations 1. Convert the following log & exponential equations Log equationExponential Equation Log equationExponential Equation Log 2 16 = 4 Log 2 16 = 4 Log 3 1 = 0 Log 3 1 = 0 ?5 2 = 25 ?5 2 = 25

Warm-up 2. Solve these log expressions: 2. Solve these log expressions: Log 2 64 Log 2 64 log 9 9 log 9 9 log 3 (1/9) log 3 (1/9)

Property of Exponential Equality x m = x n ; if and only if m = n x m = x n ; if and only if m = n You will use this property a lot when trying to simplify. You will use this property a lot when trying to simplify.

Example 1: Solve 64 = 2 3n+1 64 = 2 3n+1 We want the same base (2). Can we write 64 as 2 ? We want the same base (2). Can we write 64 as 2 ? 64 = 2x2x2x2x2x2 = = 2x2x2x2x2x2 = = 2 3n = 2 3n+1 6 = 3n = 3n + 1 3n = 5 3n = 5 n = 5/3 n = 5/3

Example 2: Solve 5 n-3 = 1/25 5 n-3 = 1/25 We want the same base (5). Can we write 1/25 as 5 ? We want the same base (5). Can we write 1/25 as 5 ? 25 = 5x5 = = 5x5 = 5 2 1/25 = 1/5 2 = /25 = 1/5 2 = n-3 = n-3 = 5 -2 n – 3 = -2 n – 3 = -2 n = 1 n = 1

Using Log Properties to Solve Equations Section 3-3 Pg

Objectives I can solve equations involving log properties I can solve equations involving log properties

3 Main Properties Product Property Product Property Quotient Property Quotient Property Power Property Power Property

Product Property of Logarithms

Example Working Backwards Solve the following for “x” Solve the following for “x” log log 4 6 = log 4 x log log 4 6 = log 4 x log 4 26 = log 4 x log 4 26 = log 4 x 26 = x 26 = x x = 12 x = 12

Product Property

Quotient Property of Logs

Working Backwards Log Log 3 12 Log Log 3 12 Log 3 6/12 Log 3 6/12 Log 3 1/2 Log 3 1/2 Condensing an expression Condensing an expression

Quotient Property

Quotient Property Backwards Solve the following for x Solve the following for x log 5 42 – log 5 6 = log 5 x log 5 42 – log 5 6 = log 5 x log 5 42/6 = log 5 x log 5 42/6 = log 5 x x = 42/6 x = 42/6 x = 7 x = 7

Power Property of Logs

Example Power Property 4 log 5 x = log log 5 x = log 5 16 log 5 x 4 = log 5 16 log 5 x 4 = log 5 16 x 4 = 16 x 4 = 16 x 4 = 2 4 x 4 = 2 4 x = 2 x = 2

Power Property

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Homework WS 6-3 WS 6-3