College Algebra, 2013a

466 Exponential and Logarithmic Functions
6.4.1 Exercises
In Exercises 1 - 24, solve the equation analytically.
1. log(3x − 1) = log(4 − x) 2. log 2
(
x
3 ) =log 2 (x)
3. ln ( 8 − x 2) =ln(2− x) 4. log 5
(
18 − x
2 ) =log 5 (6 − x)
5. log 3 (7 − 2x) =2 6. log1 (2x − 1) = −3
2
7. ln ( x 2 − 99 ) =0 8. log(x 2 − 3x) =1
( ) 3x − 2
9. log 125 = 1 2x +3 3
11. − log(x) =5.4 12. 10 log
( x
)
10. log
10 −3 =4.7
( x
10 −12 )
= 150
13. 6 − 3log 5 (2x) = 0 14. 3 ln(x) − 2=1− ln(x)
15. log 3 (x − 4) + log 3 (x + 4) = 2 16. log 5 (2x +1)+log 5 (x +2)=1
17. log 169 (3x +7)− log 169 (5x − 9) = 1 2
18. ln(x +1)− ln(x) =3
19. 2 log 7 (x) =log 7 (2) + log 7 (x + 12) 20. log(x) − log(2) = log(x +8)− log(x +2)
21. log 3 (x) =log1 (x) + 8 22. ln(ln(x)) = 3
3
23. (log(x)) 2 =2log(x) + 15 24. ln(x 2 )=(ln(x)) 2
In Exercises 25 - 30, solve the inequality analytically.
1 − ln(x)
25.
x 2 < 0 26. x ln(x) − x>0
( x
)
( x
)
27. 10 log
10 −12 ≥ 90
28. 5.6 ≤ log
10 −3 ≤ 7.1
29. 2.3 < − log(x) < 5.4 30. ln(x 2 ) ≤ (ln(x)) 2
In Exercises 31 - 34, use your calculator to help you solve the equation or inequality.
31. ln(x) =e −x 32. ln(x) = 4√ x
33. ln(x 2 +1)≥ 5 34. ln(−2x 3 − x 2 +13x − 6) < 0