MATH 112 WORK SHEET 20: Logs And Exponential Problems

Laws of Logs

1. log (ab) = log a + log b

2. log (a / b) = log a - log b

3. log aⁿ = n log a

log_c b

4. log_ab = -------------

log_c a

Use Laws of Logs to Expand

1.

2.

3.

4.

5.

6.

7.

Contract using the Laws of logs

8. log 3 + log 4 - 2log 5

9. log 4 + log π + 3log r - Log3

10. log π + 2 log r

11. -2 log 5 + log 13 + log 2³

12. .5[log a - 3log b + log(c-a)]

13. -2log 4 + 1/3log 9 + 1/2log7

Solve for x

14. 2^{x + 1} = 128

15. 30^{x + 4} = 810000

16. (.01)^x = 3

17. 4 ^{2x + 1}= 7^{2x - 1}

18. 3^{2x + 3}= 8^{3x - 4}

19. log (x + 3)²= 2

20. log (13 + 2x)⁷= 14

21. log(3x + 4)-log(2x - 2) = 2

22. log(x²- 16) - log(x-4) = 2

23. log₂(x + 1) + log₂(x - 1) = 3

24. log x - log (x+4) = .3010

25. x^{log x}= 10

Answer key to the logorithm worksheet

1. 1/3 log x + log (1 + x)

2. log x + 1/2 log (x-1)

3. 3log x + log y - log z

4. 1/2[log (x-1) - log(x+1)]

5. 3[log(x-3)-log(x-2)-log(x+2)]

6. 3/5ln(x-3) +1/2ln(x+2)-1/3ln(x+3)

7. 5ln x + 8ln y -1/2ln z

8. log(12/25)

4πr³

9. log-----

3

10. log πr²

11. log(104/25)

12.

13.

14. 6

15. 0

16. -.2386

17. 2.978

18. 2.874

19. 7 or -13

20. 87/2

21. 204/197

22. 96

23. 3

24. no solution

25. 10 or .1