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7.4 Solve Exponential and Logarithmic Equations
Solve the exponential equation. Check for extraneous solutions. Round the result to
three decimal places if necessary.
1. ex = 1
9. 7 2 x  3 4 = 1 4
2. e x + 1 = 7
10. 4e3x = 1
3. 5x = 12
11. e5x + 2
4. 4 x  6 = 4
12. 92x = 32x + 4
5. 34x = 27
13. 3(2x + 6 )=17
6. 102x3 + 3 = 19
14. 50.5x + 12 = 21
7.
3ex + 7 = 9
15. 102x+1 + 2 = 2
8.
82x = 8x + 7
=
e3x+12
Solve the logarithmic equation. Check for extraneous solutions. Round the result
to three decimal places if necessary.
16. log x = 3
24. 3 ln x  7 = 4
17. ln x = 4
25. ln(l  3x) + 3 = 9
18. log3 x = 5
26. log 7x + 4 = 5
19. log7(2  x) = log7 5x
27. 4 + log9 (3x  7) = 6
20. ln(5  2x) = ln(5x + 3)
28. log2 2x + log2 x = 5
21. log4 3x = 6
29. log6(2x - 6) + log6 x = 2
22. 7  log3 8x = 2
30. ln 3x - In 2 = 4
23. 2 log7 (l  2x) = 12