Logarithmic and Exponential Equations

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Presentation transcript:

Logarithmic and Exponential Equations 13 Logarithmic and Exponential Equations

What you should learn: I can solve logarithmic and exponential equations when the bases cannot be made the same!

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