Exponents and Logarithms

Exponent Laws

100

3x^{4 *} 12x³

36x⁷

200

(x⁵y³)/(x²y²)

x³y

300

(2/5)³

8/125

400

(3x)²/(6x)

3x/2

500

(3x^-2 y⁴)/(x^-5 y^-3)

3x³y⁷

Solving equations using exponent laws

100

27=3^x

x=3

200

2⁴=2^x

x=4

300

(1/5)^x = 125

x = -3

400

8^x = 2^x-4

x = -2

500

3^x * 9^x-2 = 81^x

x = -4

Logarithms <-> Exponents

100

log₃ 9 = x

2 = x

200

log₄ 1

0 = x 

300

log₇ (1/49)

-2 = x 

400

log₃ (x) = 3

27 = x

500

log_x (1/16) = -4

x = 2

Solving equations using logs

100

3^x = 100

x = 4.19

200

7^x-2 = 47

x = 3.98

300

6^3x-7 = 234

x = 3.35

400

2* 3^x - 7 = 38

2.83 = x

500

0.5* 5^2x-3 + 1 = 199

x = 3.36

Applications

100

Does a growth factor of 0.7 indicate growth or decay? 

Decay

200

The population of a country is growing by 1.2% per year. Give the growth factor. 

1.012

300

The model A = 300(1.02)^x can be used to show how much money, in euros, you have in a savings account after x years. How much did you start with?

300€

400

The model A = 300(1.02)^x can be used to show how much money, in euros, you have in a savings account after x years. Is the amount of money increasing or decreasing? By what percentage per year? 

increasing by 2% per year

500

The model A = 300(1.02)^x can be used to show how much money, in euros, you have in a savings account after x years. After approximately how many years will you have more than 400€?

14.5 years