Exponential Equations Practice

Same Base (no calculator)

100

2^x=32

x=4

200

3^x+1=81

x=3

300

5^2x=125

x=3/2

400

4^x-1=64

x=4

500

8^x+1=512

x=2

Rewrite the Number (no calculator)

100

9^x=27

x=3/2

200

16^x=8

x=3/4

300

25^x-1=125

x=5/2

400

27^2x=81

x=2/3

500

32^x=4^x+1

x=2

Logs & Decimals

100

10^x=50

x=1.7

200

7^x=100

x=2.37

300

3^x+2=20

x=0.73

400

2^4x-2=19

x=1.56

500

6×2^x=45

x=2.91

Word Problems

100

A bacteria culture doubles every hour. If it starts with 5 bacteria, how long until there are 40?

3 hours

200

A population triples every 2 years. Starting at 100 people, how long until there are 900?

4 years

300

A savings account grows by a factor of 2 every 5 years. How long until $200 becomes $1600?

15 years

400

A culture starts with 80 bacteria and doubles every 4 hours. How long until there are 640 bacteria?

12 hours

500

A phone battery loses half its charge every 3 hours. Starting at 100%, how long until it reaches 12.5%?

9 hours

Challenge Problems

100

2^x+1=3^x

x=2.71

200

5^x=2^x+3

x=3.42

300

10^2x=7

x=0.42

400

4^x=7^x-1

x=2.43

500

3^2x+1=50

x=1.45