Free Printable Unit 1 - Solving Exponential Equations

1.

What is the value of x in the equation $2^6 ÷ 2^x = 8$ ? The value of x is (a) ?

2.

In the equation $3^{-4} \times 81 = 3^{x}$ , the value of x is (a) .

3.

The value of x in the equation $a^x a^8 = 1$ is (a) .

4.

In the equation $4\times8^{x+1}=2^{2x}$ , the value of x is (a) .

5.

The value of x in the equation $(a^x)^2 \times a^5 = a^{3x}$ is (a) .

6.

In the equation $2^x=\frac{2^{10}}{16^x}$ , the value of x is (a) .

7.

The value of x in the equation $3^6\div3^x=81^{\left(x+1\right)}$ is (a) .

8.

In the equation $(m^2)^x \times m^{(x+1)} = m^{-2}$ , the value of x is (a) .

9.

The value of x in the equation $25^x\div125=\frac{1}{5^x}$ is (a) .

10.

Solve

a)

2

b)

-2

c)

3

d)

-3

11.

To solve 36 = 6^x, re-write 36 as what base and exponent?

a)

3⁶

b)

6³

c)

6²

d)

3¹²

12.

To solve 8 = 2^5x+7, you would need to re-write 8 as what base?

a)

8

b)

4

c)

2

d)

Cannot be determined

13.

Solve 8 = 2^5x+7

a)

⅘

b)

¼

c)

-⅘

d)

-¼

14.

Solve 3³ = 3^{4x + 2}

a)

¼

b)

-¼

c)

½

d)

-½

15.

Solve for n:
2^-2n = 2⁶

a)

-1

b)

-7

c)

5

d)

-3

16.

Solve for b:
4^{3b - 3} = 1/16

a)

7

b)

-1/4

c)

1/2

d)

1/3

17.

Solve for r:
3^-3r = 3⁵

a)

-4

b)

-5/3

c)

2

d)

8

18.

Solve for x:
3^2x = 27

a)

3/2

b)

-2

c)

0

d)

5

19.

Solve for p:
4^p+2 = 64

a)

-16/9

b)

1

c)

8

d)

7/6

20.

Solve for a:
5^{a + 2} = 1/125

a)

-1

b)

-6/7

c)

-5

d)

4

Unit 1 - Solving Exponential Equations

Total questions: 20

Worksheet time: 2hrs 40mins

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