Free Printable Solving Simple Exponential Equations Word Problems With Common Bases

1.

Solve 3²⁶ = 3^{4x + 2}

a)

x = 6

b)

x = 5

c)

x = 3

d)

x = -4

2.

Solve for x:
5^2x = 5^-x

a)

0

b)

-6

c)

8

d)

1

3.

Solve for x:
(-3)^x = (-3)¹³

a)

13

b)

-3

c)

x + 13

d)

x -13

4.

Solve 3³ = 3^{4x + 2}

a)

x = ¼

b)

x = -¼

c)

x = ½

d)

x = -½

5.

8^3x+3 = 8⁶

a)

x=28

b)

x=3

c)

x=1

d)

x=12

6.

Solve 8 = 2^5x+7

a)

x = ⅘

b)

x = ¼

c)

x = -⅘

d)

x = -¼

7.

Solve for n:
2³ⁿ = 4

a)

2

b)

3

c)

2/3

d)

4

8.

Solve: 7^-x = 49

a)

1

b)

-1

c)

2

d)

-2

9.

3^{2x – 6} = 81

a)

x = log 4

b)

x = 5

c)

x = 4

d)

x = -1

10.

Solve the following exponential equation:
$5^{-3x}=125$

a)

$x=-1$

b)

$x=-4$

c)

$x=-3$

d)

$x=1$

11.

How would you solve an exponential equation like the one below:

36=6^x

a)

Rewrite $36$ as $6^2$

b)

Set the exponents equal to each other

c)

Rewrite $36$ as $6^3$

d)

Multiply the exponents

12.

Solve the following exponential equation:

2^{x+6}=32

a)

$x=-1$

b)

$x=-2$

c)

$x=1$

d)

$x=2$

13.

Solve for x: 2^x = 16

a)

4

b)

3

c)

2

d)

1

14.

Solve for x : 4^x = 64

a)

1

b)

2

c)

3

d)

4

15.

Solve for x.
3^x = 27

a)

2

b)

4

c)

3

d)

5

16.

Sovle for x:
5^{-3x - 1} = 25

a)

x = -1

b)

x = -4

c)

x = -3

d)

x = 1

17.

Solve

3^{\left(x+1\right)}=27.

a)

$x=2$

b)

$x=4$

c)

$x=-4$

d)

$x=-2$

18.

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

a)

3⁶

b)

6³

c)

6²

d)

3¹²

19.

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

20.

Solve for r:
3^-3r = 3⁵

a)

-4

b)

-5/3

c)

2

d)

8

21.

Rewrite 64 as a power of 2:

a)

$2^2$

b)

$2^6$

c)

$4^3$

d)

$2^8$

22.

Rewrite

\frac{1}{36}

as a power of 6.

a)

6

b)

$6^2$

c)

$6^6$

d)

$6^{-2}$

Solving Simple Exponential Equations Word Problems With Common Bases

Total questions: 22

Worksheet time: 2hrs 50mins

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