Logarithmic and Exponential Equations

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Presentation transcript:

Logarithmic and Exponential Equations 6 Logarithmic and Exponential Equations

2.7 I can solve logarithmic equations. What you should learn: 2.7 I can solve logarithmic equations.

Equality Property of Logarithms We will use this along with the other properties of logs to solve logarithmic equations.

Check!

Check x = 3. Argument > 0 Both terms are undefined. Solution set {x | x = 3}.

Log4(3x + 4) = Log4(5x – 6) (3x + 4) = (5x – 6) 4 = 2x – 6 10 = 2x 5 = x

Log2(x2 - 9) = Log2(x + 3) (x2 - 9) = (x + 3) x2 – x - 12 = 0 (x – 4)(x + 3) = 0 x – 4 = 0 x + 3 = 0 x = 4 or x = -3

x = -3 Log2((-3)2 - 9) = Log2(-3 + 3) Log2(x2 - 9) = Log2(x + 3) Check! x = -3 Log2((-3)2 - 9) = Log2(-3 + 3) Can not use this answer! Argument > 0 x = 4 Log2((4)2 - 9) = Log2(4 + 3) Log2(7) = Log2(7) x = 4