1. Logarithmic and Exponential Equations6
Logarithmic and Exponential Equations

2. 2.7 I can solve logarithmic equations.
What you should learn:
2.7 I can solve logarithmic equations.

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

5. Check!

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

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

8. 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

9. x = -3 Log2((-3)2 - 9) = Log2(-3 + 3)
Log2(x2 - 9) = Log2(x + 3)
Check!
x = 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