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© h.hofstede (h.hofstede@hogeland.nl) |
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| 1. | a. | 2log(5) + 2log(6) = 2log(5 · 6) = 2log(30) | |
| b. | 3·logx + 7·logx = log(x3) + log(x7) = log(x10) | ||
| c. | 0,1 · 6logx - 6logx = -0,9×6log(x) = 6log(x-0,9) | ||
| d. | 2logx - 2log(2x) + 2log(3x) = 2log(x × 3x/2x) = 2log(1,5x) | ||
| e. | -4logx - 4log(x3) = 4log(x-1) - 4log(x3) = 4log(x-4) | ||
| f. | 5log2 + 3 • 5log4 = 5log2 + 5log(43) = 5log(2 × 43) = 5log(128) | ||
| g. | 4 • 5logx + 5log6 = 5log(x4) + 5log(6) = 5log(6x4) | ||
| h. | 3log(x) - 3log(x + 2) = 3log(x/(x + 2)) | ||
| i. | 4 • logx + 3 • log5 = log(x4) + log(53) = log(x4 × 53) = log(125x4) | ||
| j. | 2 · 0,5log(2x) + 0,5log(x2) = 0,5log(4x2) + 05log(x2) = 0,5log(4x4) | ||
| 2. | log(75!) = log(75 × 74 × 73 × 72 × 71 × 70 × 69!) = log75 + log74 + log73 + log72 + log71 + log70 + log(69!) = 109,3946... Dus 75! = 10109,3946 = 10109 × 100,3946 = 2,48 × 10109 |
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| 3. | log(1000 • x3/√y) = log(1000) + log(x3) - log(y0,5) = 3 + 3log(x) - 0,5log(y) = 3 + 3 × 5 - 0,5 × 0,5 = 17,75 |
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