Dr. J's Maths.com
Where the techniques of Maths
are explained in simple terms.
Where the techniques of Maths
are explained in simple terms.
Functions - Logarithmic function - Concept and simplifying expressions.
Test Yourself 1.
- Algebra & Number
- Calculus
- Financial Maths
- Functions & Quadratics
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- Trigonometry
- Maths & beyond
- Index
1. Change each of the following expressions from exponential to logarithmic form:
| 1. 9 = 32
Answer.log39 = 2. |
2. 10,000 = 104
Answer.log10 10,000 = 4. |
3. x = a2
Answer.loga x = 2. |
| 4. a = b(2x-1)
Answer.logb a = (2x - 1). |
5. (3z+1) = 10x
Answer.log10 (3z + 1) = x. |
6. (x - y) = m5
Answer.logm (x - y) = 5. |
| 7. 5x = 4
Answer.log5 4 = x. |
8. 2x - 3 = 4y
Answer.log2 (4y + 3) = x. |
9. 1.005n = x |
2. Change each of the following expressions from logarithmic to exponential form and solve for x:
| 10. log2 x = 8
Answer.x = 28 = 256. |
11. log5 x = 0
Answer.x = 50 = 1. |
12. log3 x = -2
Answer.x = 3-2 = 1/9. |
| 13. log10 (2x) = 2
Answer.2x = 102 ∴ x = 50. |
14. log4 (x-1) = 1
Answer.x - 1 = 41 ∴ x = 5. |
15. Answer.3-3 = 3x ∴ x = -3. |
3. Evaluate each of the following without using a calculator.
Hint.Set each expression equal to x and then convert to exponential format.
| 16. log2 128
Answer.Log2128 = log22 7 = 7log22 = 7. |
17. log3 9
Answer.log3 9 = log33 2 = 2log33 = 2. |
18. logm m
Answer.logm m = 1. |
19. 
Answer.log3 31/2 = 1/2. |
20. log5 0.25
Answer.log5 (5/10)-2 = -2log5 2. |
21. 3 log525
Hint.Reqrite 25 as 52. Simplify then multiply by 3. Answer.3log5 25 = 3log5 52 = 6. |
4.
| 22. Show that elnx = x. | 23. Write down the value of eln 5
Answer.5. |
24. Evaluate 4eln3
Answer.24. |
| 25. If e4x = 4, show that
x = ½ln 2 |
26. Find the solutions for the equation
(logex - 4)(logex +2) = 0 Answer.x = e4 or x = e-2. |
27. Solve
(logex)2 - 2logex = 8 Answer.x = e4 or x = e-2. |
| 28. Solve for x:
4e2x - ex = 0. Answer.x = -2ln2 but 3x ≠ 0. |
29. Show that
|
30. |
