NAME
DATE
7-7
PERIOD
Skills Practice
Base e and Natural Logarithms
Write an equivalent exponential or logarithmic equation.
x = ln 3
3. ln 15 = x
e x = 15
5. e4 = x - 3 ln (x – 3) = 4
2. e4 = 8x
4 = ln 8x
4. ln x ≈ 0.6931
x ≈ e0.6931
6. ln 5.34 = 2x 5.34 = e2x
Write each as a single logarithm.
7. 3 ln 3 - ln 9 ln 3
9. 2 ln x + 2 ln 4 ln 16x2 or 2 ln 4x
8. 4 ln 16 - ln 256 ln 256 or 2 ln 16
10. 3 ln 4 + 3 ln 3 3 ln 12
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Solve each equation or inequality. Round to the nearest ten-thousandth.
11. ex ≥ 5
{x | x ≥ 1.6094}
12. ex < 3.2
{x | x < 1.1632}
13. 2ex - 1 = 11 1.7918
14. 5ex + 3 = 18 1.0986
15. e3x = 30 1.1337
16. e-4x > 10
17. e5x + 4 > 34
19. ln 3x = 2
{x | x > 0.6802}
2.4630
{x | x < -0.5756}
18. 1 - 2e2x = -19 1.1513
20. ln 8x = 3 2.5107
21. ln (x - 2) = 2 9.3891
22. ln (x + 3) = 1 -0.2817
23. ln (x + 3) = 4 51.5982
24. ln x + ln 2x = 2 1.9221
Chapter 7
49
Glencoe Algebra 2
Lesson 7-7
1. ex = 3