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| OPGAVEN |
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| 1. |
Los algebraïsch op: 5 • 2x +
1 - 15 = 0 |
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| 2. |
Los algebraïsch op: 4 • 3log x
- 8 = 0 |
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| 3. |
Los algebraïsch op: 2 • 3log x
= 3log (x - 2) + 2 |
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| 4. |
Gegeven is, dat p = 6 • 2q
. Daaruit volgt dat q = a + 2 log p
. Bereken algebraïsch a. |
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| OPLOSSING |
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| 1. |
5 • 2x +
1 - 15 = 0
Þ 5 • 2x + 1 = 15
Þ 2x + 1 = 3
Þ x + 1 = 2 log
3
Þ x
= 2 log 3 - 1 (» 0,58) |
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| 2. |
4 • 3log x
- 8 = 0
Þ 4 • 3 log x = 8
Þ 3 log x = 2
Þ x = 32 =
9 |
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| 3. |
2 • 3log x
= 3log (x - 2) + 2
Þ 3log x2 -
3 log(x - 2) = 2
Þ 3log (x²/(x-
2)) = 2
Þ x²/(x-
2) = 32 = 9
Þ x2 = 9(x -
2) = 9x - 18
Þ x2 - 9x
+ 18 = 0
Þ (x - 6)(x - 3) = 18
Þ x
= 6 V x = 3 |
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| 4. |
p = 6 • 2q
Þ p/6 = 2q
Þ q = 2log(p/6)
= 2 log p - 2log 6 dus a
= - 2 log 6 (» -2,58) |
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