Logarithmic and Exponential Equations

Logarithmic Equations

100

4^x  =  16

x = 2

200

7^x  =  23

x = 1.6

300

log 15 = log (2x+3)

x = 7

400

14^m  =  153

m = 1.9

500

log (3x-15) = log (6x+3)

x = 6

Logarithmic Equations 2

100

log_x 4x = 3

x = 54

200

log_x 49 = 7

x = 7

300

log₃ 5x = 3

x = 27/5

400

log₈ (5x+1) = log₈ (x-5)

x = -1

500

log₆ 4x = 3

x = 54

Exponential Growth and Decay (Use desmos.com/scientific)

100

A car's price of $12,500 decreases 9% each year, how much would the car be worth after 5 years?   Exponential Decay equation: f(x) = a(1 - r)^t

f(x) = 7200.40

200

A computer's valued price of $6500 decreases by 14% per year, what would be its price after 3 years? Exponential Decay Equation: f(x) = a(1 - r)^t

f(x) = 4134.36

300

An insect population increases at a rate of 2% per year. There are 1,573 insects this year, how many insects will there be in 10 years? Exponential Growth Equation: f(x) = a(1 + r)^t

f(x) = 1917.47

400

An ancient antique valued at a price of $14,000 has an increase rate of 5% per month how much will it be worth after 7 months? Exponential Growth Equation: f(x) = a(1 + r)^t

f(x) - 19,699.40

500

A sculpture worth $13,300 has a decrease rate of 43% per year. How much will the sculpture be worth in 5 years?

f(x) = 505.67