Functions - Logarithmic functions - Log Laws.
Test Yourself 2.
Use the six laws of logarithms as outlined in the video to simplify/solve the following:
Log laws with numbers. | 1. Simplify log2 48 - log2 3.
Answer.4. |
2. Evaluate correct to 3 significant figures:
log4 32 - log4 5.
Answer.1.34. |
3. Find the value of log5 200 - 3log5 2.
Answer.2. |
4. | |
5. Simplify . Answer.-2. |
6. Find the value of J (to 2 decimal places) if log3 5 + log2 9 = J Answer.4.63. |
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7. If ,
find the values of p and q. Answer.p = 5 and q = -3. |
8. Show . | |
Log laws with pronumerals. | 9. Simplify log3 81x - log3 9x
Answer.2. |
10. |
11. Simplify .
Answer.2. |
12. If log x + log y = log (x+y), prove
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15. | 16. | |
17. If where a > 0 and N > 0, show y = loga N. |
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19. Change the subject of the following equation to y in a form not involving any logarithms:
2log2 x + log2 y = 3. Answer.y = 8/x2 |
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21. | 22. | |
23. | 24. | |
25. | 26. | |
27. Simplify . Answer.value = 1. |
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Substitution | 29. If log pq = 1.544 and log qr = 1.113, find the value of . Answer.value = 0.431. |
30. If log 2 = a and log 3 = b and log 5 = c, express each of the following in terms of a, b and c: (i) log 45 (ii) (iii) . (iv) . Answer.(i) 2b + c.(ii) a + b - 2c (iii) 1/2(2a + 2c - 3b) (iv) 1/4(a - 2c). |
31. It is given that loga b = 2.75 and that loga c = 0.25. Hence find the value of Answer.(i) 2.5. (ii) 6. |
32. Given x = log10 2 and y = log10 3 find in terms of x and y:
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Equations | 33. If y = loga (7x - b)+ 3 , change the subject of the equation to x. | 34. Solve 2 ln x = ln (5 + 4x).
Answer.x = 1 but x ≠ -5. |
35. Solve log10 x2 + 3 = log10 x5 Answer.x = 10. |
36. Solve 2log5 3 = log5 x - log5 6. |
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37. Solve 2log2 x - log2 (x+4) = 1 | 38. Solve loge x - loge (x-4) = loge 2 | |
39. Solve (log10 x3)(log10 x) + log10 x4 - 7 = 0 |
40. Solve log3 (2x - 7) = 2.
Answer.x = 8. |
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41. Solve log5 (4 - x) = 1 + 2 log5 x
Answer.x = 4/5. |
42. Solve 3log72 = log7x - log75. |