1. 7.6 – Solve Exponential and Log Equations

2. Property of Equality for Exponential Equations
If b is a positive number other than 1,
then ___________ if and only if
___________.

3. Solve the equation. 1.
3x – 4 = 5
3x = 9
x = 3

4. Solve the equation. 2.
3x – 8 = 4(13 – 3x)
3x – 8 = 52 – 12x
15x – 8 = 52
15x = 60
x = 4

5. Solve the equation. 3.
3(4x – 1) = 2(3x + 8)
12x – 3 = 6x + 16
6x – 3 = 16
6x = 19

6. Solve the equation. 4.
2x = –(x – 3)
2x = –x + 3
3x = 3
x = 1

7. How to solve for a power
To eliminate the power, take the log of both sides. It lowers the exponent.

8. Solve the equation. 5.

9. Solve the equation. 6.

10. Solve the equation. 7.

11. Solve the equation. 8.

12. Property of Equality for Logarithmic Equations
If b is a positive number
other than 1, then
__________________ if and
only if ___________.

13. Solve the equation. Check for extraneous solutions.9.
5x + 9 = 6x
9 = x

14. Solve the equation. Check for extraneous solutions.
10.
5x + 18 = 7x – 8
18 = 2x – 8
26 = 2x
x = 13

15. Solve the equation. Check for extraneous solutions.
11.
12x – 11 = 3x + 16
9x – 11 = 16
9x = 27
x = 3

16. 12. No solution 3x – 10 = 14 – 5x 8x – 10 = 14 8x = 24 x = 3
Solve the equation. Check for extraneous solutions.
12.
No solution
3x – 10 = 14 – 5x
8x – 10 = 14
8x = 24
x = 3

17. How to solve for a Log
To eliminate the log, raise both sides to the base power. This eliminates the log.
b b

18. Solve the equation. Check for extraneous solutions.
13.
x – 6 = 25
25 = 32
x – 6 = 32
x = 38

19. Solve the equation. Check for extraneous solutions.
14.
42 = 16
8x = 42
8x = 16
x = 2

20. Solve the equation. Check for extraneous solutions.
15.
43 = 64
x(x + 12) = 43
x2 + 12x = 64
x2 + 12x – 64 = 0
(x + 16)(x – 4) = 0 x 16 x
x = 4, -16 -4

21. Solve the equation. Check for extraneous solutions.
16.
102 = 100
5x(x – 1) = 102
5x2 – 5x = 100
5x2 – 5x – 100 = 0
5(x2 – x – 20) = 0 x -5
5(x – 5)(x + 4) = 0 x 4
x = 5, -4