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| 1. | a. | 27x • 3 = 9 (33)x • 3 = 32 33x • 31 = 32 33x + 1 = 32 3x + 1 = 2 3x = 1 x = 1/3. |
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| b. | √125 =
25x • 5x + 1 √(53) = (52)x • 5x + 1 (53)0,5 = 52x • 5x + 1 51,5 = 52x + x + 1 1,5 = 2x + x + 1 0,5 = 3x x = 1/6 |
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| c. | 16 • 42x = 23x
• 8x 24 • (22)2x = 23x • (23)x 24 • 24x = 23x • 23x 24 + 4x = 23x + 3x 4 + 4x = 6x 4 = 2x x = 2 |
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| d. | 3 • 9x = 81x
- 3 3 • (32)x = (34)x - 3 31 • 32x = 34x - 12 31 + 2x = 34x - 12 1 + 2x = 4x - 12 13 = 2x x = 61/2 |
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| e. | (1/2)3x
= (1/4)x
- 4 (1/2)3x = ((1/2)2)x - 4 (1/2)3x = (1/2)2x - 8 3x = 2x - 8 x = -8 |
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| f. | 6x • 36x
= √216 6x • (62)x = √(63) 6x • 62x = (63)0,5 6x + 2x = 61,5 x + 2x = 1,5 x = 1/2 |
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| 2. | a. | 2 = 4 - 20,3x - 2 -2 = -20,3x - 2 2 = 20,3x - 2 21 = 20,3x - 2 1 = 0,3x - 2 0,3x = 3 x = 10 |
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| b. |
4 - 20,3x - 2
= 0 20,3x - 2 = 4 20,3x - 2 = 22 0,3x - 2 = 2 0,3x = 4 x = 131/3. Dus Q = (131/3, 0) P = (0,5) dus PQ heeft helling (5 - 0)/(0-13,333) = -3/8 l is de lijn y = -3/8x + 5 Y1 = (3/8)*X + 5 en Y2 = 4 - 2^(0.3*x - 2) en dan intersect geeft x = 4,30 en y = 3,39 S = (4.30 , 3.39) |
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| c. | 20 naar links: x vervangen door
x + 20 10 omhoog: hele formule + 10 Dat geeft g(x) = 4 - 20,3(x + 20) - 2 + 10 g(x) = 14 - 20,3x + 6 - 2 g(x) = 14 - 20,3x + 4 g(x) = 14 - 20,3x • 24 g(x) = 14 - 16 • 20,l3x Dus a = 14 en b = -16 |
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© h.hofstede (h.hofstede@hogeland.nl) |
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