1. Logarithmic and Exponential Equations13
Logarithmic and Exponential Equations

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

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