EXPONENTIAL EQUATIONS WORKSHEET 

Solve each of the following exponential equations.

Problem 1 :

4^{x + 1} = 32

Problem 2 :

Problem 3 :

Problem 4 :

Problem 5 :

2(4^{2x + 1}) = 128

Problem 6 :

√5 = 5^{x + 4}

Problem 7 :

2^x + 2^{1 - x} = 3

Problem 8 :

Problem 9 :

Problem 10 :

Answers

1. Answer :

4^{x + 1} = 32

(2²)^{x + 1} = 2⁵

2^{2(x + 1)} = 2⁵

2^{2x + 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} = 9^{2x - 1}

3^{-3(4 - x)} = (3²)^{2x - 1}

3^{-12 + 3x} = 3^{2(2x - 1)}

3^{-12 + 3x} = 3^{4x - 2}

-12 + 3x = 4x - 2

x = -10

3. Answer :

3^{12x + 8 - 5x} = 3

3^{7x + 8} = 3¹

7x + 8 = 1

7x = -7

x = -1

4. Answer :

6^{-3x - 6 - 9x} = 6^-3

6^{6x - 6} = 6^-3

6x - 6 = -3

6x = 3

x = ½

5. Answer :

2(4^{2x + 1}) = 128

2(2^{2(2x + 1)}) = 128

2^{2(2x + 1)} = 64

2^{4x + 2} = 2⁶

4x + 2 = 6

4x = 4

x = 1

6. Answer :

7. Answer :

Let y = 2^x.

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

8. Answer :

7^{2x + 1} = 7^-2

2x + 1 = -2

2x = -3

x = ³⁄₂

9. Answer :

3^{2x + 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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