Chapter 7: Exponential Functions
Section 7.2: Exponential Equations
#1 - 42: Solve the exponential equation by writing each side of the equation with the same base then
equating the exponents.
1) 2x = 16
2x = 24
Solution: x = 4
3) 2x = 32
2x = 25
Solution: x = 5
5) 3x = 27
3x = 33
Solution: x = 3
7) 24−𝑥 = 64
24-x = 26
4–x=6
-6 +x -6 + x
-2 = x
Solution: x = -2
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Chapter 7: Exponential Functions
9) 26-x = 16
26-x = 24
6–x=4
-4 +x -4 + x
2=x
Solution: x = 2
11) 16x = 4
(24)x = 22
24x = 22
4x = 2
2
𝑥=4
𝟏
Solution: x = 𝟐
13) 64x = 2
(26)x = 21
26x = 21
6x = 1
𝑥=
1
6
𝟏
Solution: x = 𝟔
15) 25x-3 = 5
(52)x-3 = 51
52x-6 = 51
2x - 6 = 1
2x = 7
𝟕
Solution: x = 𝟐
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Chapter 7: Exponential Functions
1 𝑥
17) (2) = 16
(I need to know that ½ = 2-1 to get through this problem)
(2-1)x = 24
2-1x = 24
-1x = 4
Solution: x = -4
1 𝑥
19) (4) = 256
(I need to know that 1/4 = 4-1 to get through this problem)
(4-1)x = 256
(4)-1x = 28
(22)-1x = 28
2-2x = 28
-2x = 8
Solution: x = -4
1 𝑥
21) (3) = 81
(I need to know that 1/3 = 3-1 to get through this problem)
(3-1)x = 34
3-1x = 34
-1x = 4
Solution: x = -4
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Chapter 7: Exponential Functions
1 𝑥+1
23) (2)
=8
(I need to know that ½ = 2-1 to get through this problem)
(2-1)x+1 = 23
2-1x-1 = 23
-1x -1 = 3
-1x = 4
Solution: x = -4
1 𝑥−7
4
25) ( )
= 256
(4-1)x-7 = 256
(4)-x+7 = 28
(22)-x+7 = 28
2-2x+14 = 28
-2x +14= 8
-2x = -6
Solution: x = 3
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Chapter 7: Exponential Functions
1 4𝑥+1
27) (3)
= 81
(I need to know that 1/3 = 3-1 to get through this problem)
(3-1)4x+1 = 34
3-4x-1 = 34
-4x-1 = 4
-4x = 5
Solution: x = -5/4
29) 3x = 9x+1
3x = (32)x+1
3x = 32x + 2
x = 2x + 2
-x = 2
Solution: x = -2
31) 2x+4 = 162x-3
2x + 4 = (24)2x-3
2x+4 = 28x – 12
x + 4 = 8x – 12
16 = 7x
Solution: x = 16/7
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Chapter 7: Exponential Functions
33) 5x-3 = 254x-7
5x – 3 = (52)4x – 7
5x – 3 = 5 8x – 14
x – 3 = 8x – 14
11 = 7x
Solution: x = 11/7
35) 27x = 9x+1
(33)x = (32)x+1
33x = 32x + 2
3x = 2x + 2
Solution: x = 2
37) 64x+4 = 162x-3
(26)x+4 = (24)2x – 3
26x + 24 = 28x – 12
6x + 24 = 8x – 12
36 = 2x
Solution: x = 18
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Chapter 7: Exponential Functions
39) 625x-3 = 254x-7
(54)x – 3 = (52)4x – 7
54x – 12 = 58x – 14
4x – 12 = 8x – 14
2 = 4x
2/4 = x
Solution: x = 1/2
41) 16x = 327x
(24)x = (25)7x
24x = 235x
4x = 35x
-31x = 0
x = 0/(-31)
Solution: x = 0
65