Solve each of the following exponential equations.
Problem 1 :
4x + 1 = 32
Problem 2 :
Problem 3 :
Problem 4 :
Problem 5 :
2(42x + 1) = 128
Problem 6 :
√5 = 5x + 4
Problem 7 :
2x + 21 - x = 3
Problem 8 :
Problem 9 :
Problem 10 :
1. Answer :
4x + 1 = 32
(22)x + 1 = 25
22(x + 1) = 25
22x + 2 = 25
Since the above two terms are equal with the same base '2', the exponents can be equated.
2x + 2 = 5
2x = 3
x = ³⁄₂
2. Answer :
(3-3)4 - x = 92x - 1
3-3(4 - x) = (32)2x - 1
3-12 + 3x = 32(2x - 1)
3-12 + 3x = 34x - 2
-12 + 3x = 4x - 2
x = -10
3. Answer :
312x + 8 - 5x = 3
37x + 8 = 31
7x + 8 = 1
7x = -7
x = -1
4. Answer :
6-3x - 6 - 9x = 6-3
66x - 6 = 6-3
6x - 6 = -3
6x = 3
x = ½
5. Answer :
2(42x + 1) = 128
2(22(2x + 1)) = 128
22(2x + 1) = 64
24x + 2 = 26
4x + 2 = 6
4x = 4
x = 1
6. Answer :
7. Answer :
Let y = 2x.
y2 + 2 = 3y
y2 - 3y + 2 = 0
Solve by factoring.
y2 - 2y - y + 2 = 0
y(y - 2) - 1(y - 2) = 0
(y - 2)(y - 1) = 0
y - 2 = 0 or y - 1 = 0
y = 2 or y = 1
y = 2 2x = 2 2x = 21 x = 1 |
y = 1 2x = 20 2x = 20 x = 0 |
8. Answer :
72x + 1 = 7-2
2x + 1 = -2
2x = -3
x = ³⁄₂
9. Answer :
32x + 3 = 31
2x + 3 = 1
2x = -2
x = -1
10. Answer :
10-3x + x = 10-1
10-2x = 10-1
-2x = -1
x = ½
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