SOLVING EXPONENTIAL EQUATIONS USING EXPONENT PROPERTIES WORKSHEET

Solve for x in each of the following :

Problem 1 :

4x = 64

Problem 2 :

9x - 1 = 27

Problem 3 :

8x = 1

Problem 4 :

5x - 2 = ¹⁄₂₅

Problem 5 :

⋅ 2x = 72

Problem 6 :

27x - 1 = ()1 - 2x

Problem 7 :

25x + 2 ¹⁄₁₂₅

Problem 8 :

2x + 1 ⋅ 4x = (½)x + 1

Problem 9 :

3x - 1⋅ 92x + 1 = 243

Problem 10 :

9= 7(3x) + 18

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Answers

1. Answer :

4x = 64

4x = 43

x = 3

2. Answer :

9x - 1 = 27

(32)x - 1 = 33

32(x - 1) = 33

32x - 2 = 33

2x - 2 = 3

2x = 5

x = ⁵⁄₂

3. Answer :

8x = 1

8x = 80

x = 0

4. Answer :

5x - 2 = 5-2

x - 2 = -2

x = 0

5. Answer :

⋅ 2x = 72

Divide both sides by 9.

2x = 8

2x = 23

x = 3

6. Answer :

27x - 1 = ()1 - 2x

(33)x - 1 = (3-1)1 - 2x

33(x - 1) = 3-1(1 - 2x)

33x - 3 = 3-1 + 2x

3x - 3 = -1 + 2x

x - 3 = -1

x = 2

7. Answer :

52(x + 2) = 5-3

52x + 4 = 5-3

2x + 4 = -3

2x = -7

x = -⁷⁄₂

8. Answer :

2x + 1 ⋅ 4x = (½)x + 1

2x + 1 ⋅ (22)x = (2-1)x + 1

2x + 1 ⋅ 22x = 2-(x + 1)

2x + 1 + 2x = 2-x - 1

23x + 1 = 2-x - 1

3x + 1 = -x - 1

4x = -2

x = -½

9. Answer :

3x - 1⋅ 92x + 1 = 243

3x - 1⋅ (32)2x + 1 = 35

3x - 132(2x + 1) = 35

3x - 134x + 2 = 35

3x - 1 + 4x + 2 = 35

35x + 1 = 35

5x + 1 = 5

5x = 4

x = 

10. Answer :

9= 7(3x) + 18

(32)= 7(3x) + 18

(3x)= 7(3x) + 18

Let y = 3x.

y= 7y + 18

y- 7y - 18 =0

y- 9y + 2y - 18 =0

y(y - 9) + 2(y - 9) =0

(y - 9)(y + 2) = 0

y - 9 = 0  or  y + 2 = 0

y = 9  or  y = -2

y - 9 = 0

y = 9

= 32

3= 32

x = 2

y + 2 = 0

y = -2

y = -2

3= -2

In 3x, whatever real value (positive or negative or zero) we substitute for x, 3x can never be negative. So we can ignore the equation 3x = -2.

Therefore,

x = 2

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