EXPONENTIAL EQUATIONS WORKSHEET

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 :

2+ 21 - x = 3

Problem 8 :

Problem 9 :

Problem 10 :

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

(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

312x + 8 - 5x = 3

37x + 8 = 31

7x + 8 = 1

7x = -7

x = -1

6-3x - 6 - 9x = 6-3

66x - 6 = 6-3

6x - 6 = -3

6x = 3

x = ½

2(42x + 1) = 128

2(22(2x + 1)) = 128

22(2x + 1) = 64

24x + 2 = 26

4x + 2 = 6

4x = 4

x = 1

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 = 22x = 22x = 21x = 1 y = 12x = 202x = 20x = 0

72x + 1 = 7-2

2x + 1 = -2

2x = -3

x = ³⁄₂

32x + 3 = 31

2x + 3 = 1

2x = -2

x = -1

10-3x + x = 10-1

10-2x = 10-1

-2x = -1

x = ½

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