Logarithmic Test Review

Converting between Exponential & Log Functions

100

Convert 5²=25 to log form. 

log₅(25)=2

200

Convert y=b^x to log form. 

log_b(y)=x

300

Convert log₃(729)=X to exponential form. 

3^x=729

400

Convert log₂(1/16)=-4 to exponential form

2^-4=1/16

500

Convert 2^-5=1/32 into log form

log₂(1/32)=-5

Evaluating Log Functions

100

Evaluate: log⁡₇7?

1

200

Find the value of log429.7 to four decimal places

2.6332

300

Evaluate: log⁡₈1?

0

400

Evaluate to the nearest hundredth: log₂22 

4.46

500

Evaluate: log₁₂₈(1/32)

-(5/7) or -0.7142857143

Solving Exponential Equations using Logs

100

Solve for x, rounding to the nearest hundredth:3^3x=94

x = 1.38

200

Solve for x, rounding to the nearest hundredth: 92*3^4x=27

x = -0.28

300

Solve for x, rounding to the nearest hundredth: 

3(2)^(x+4)=117

x = 1.29

400

Solve for x, rounding to the nearest hundredth: 86*10^x/4=89

x = 0.06

500

Solve for x, rounding to the nearest tenth: 2100=920(1.06)^x/8+600

x = 67.1

Compounding Continuously (Time or Rate)

100

Ariana is going to invest $62,000 and leave it in an account for 20 years. Assuming the interest is compounded continuously, what interest rate, to the nearest tenth of a percent, would be required in order for Ariana to end up with $233,000?

r = 6.6%

200

Annabelle invested $5,900 in an account paying an interest rate of 2% compounded continuously. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $7,440?

t = 12

300

Ruby is going to invest $480 and leave it in an account for 9 years. Assuming the interest is compounded continuously, what interest rate, to the nearest tenth of a percent, would be required in order for Ruby to end up with $650?

r = 3.4%

400

If ae^bt=c where a, b, and c are positive, then t equals? 

ln(c/a) / b 

500

Brody invested $2,800 in an account paying an interest rate of 2.7% compounded continuously. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $3,560?

t = 9 

Compound Interest (Time or Rate) & Half Life (Time)

100

Madeline invested $2,800 in an account paying an interest rate of 4.4% compounded annually. Assuming no deposits or withdrawals are made, how long would it take, to the nearest tenth of a year, for the value of the account to reach $6,100?

t = 18.1 

200

Matthew is going to invest $82,000 and leave it in an account for 13 years. Assuming the interest is compounded monthly, what interest rate, to the nearest hundredth of a percent, would be required in order for Matthew to end up with $152,000?

r = 4.76%

300

A new car is purchased for $14,000 and over time its value depreciates by one half every 4 years. How long, to the nearest tenth of a year, would it take for the value of the car to be $200?

t = 24.5

400

Oliver is going to invest $27,000 and leave it in an account for 5 years. Assuming the interest is compounded daily, what interest rate, to the nearest tenth of a percent, would be required in order for Oliver to end up with $36,000?

r = 5.8%

500

If you deposit $8,000 into an account paying 7% annual interest compounded quarterly, how long, to the nearest hundredth of year, will it take for your money to triple?

t = 15.83