Logs and Exponential Functions with exponents

Evaluating Logs

100

Evaluate without using a calculator:

log₄64

What is 3?

200

Evaluate without using a calculator:

log₅(-125)

What is no solution.  

300

Evaluate without using a calculator:

log₂(1/64)

What is -6?

400

Evaluate without using a calculator:

log₂₇3

What is 1/3?

500

Use your calculator to evaluate:

log₅30

What is 2.113?

Evaluating Exponents

100

Evaluate without a calculator:

27^(2/3)

What is 9?

200

Evaluate without a calculator:

8^(5/3)

What is 32?

300

Evaluate without a calculator:

64^(3/2)

What is 512?

400

Evaluate without a calculator.

27^(-2/3)

What is 1/9?

500

Evaluate without using a calculator.

16^-(3/4)

What is 1/8?

Expanding and Condensing

100

Simplify:

3 log₂x + log₂ 4

What is log₂ 4x³

200

Simplify:

log₄12 + 3 log₄x - 5log₄y

What is 

log4 (12x^3)/y^5

300

Expand:

log4(x^4)/y^5

What is 4log₄x + 5log₄y?

400

Expand:

log5(sqrtx)/y

What is 1/2 log₅x - log₅y

500

Simplify:

log₃9 + 2log₃x - 6log₃y

What is 

log3 (9x^2)/y^3

Solving Equations

100

Solve:  3e^x + 4 = 16

What is 1.386?

200

Solve:  4^x+1 - 3 = 8

What is x = 0.7297?

300

Solve:

log₄(x + 3) - log₄x = 1

What is x = 1?

400

Solve:

log₃x - log₃5 = 4

What is 405?

500

Solve:  8^x+4 = 16^x

What is x = 12?

Applications

100

Suppose you invest $3000 at 5.2% interest compounded quarterly.  How much will be in the account after 5 years?

What is $3884.28?

200

Bryson bought a car for $20,000 last week.  The car depreciates at a rate of 15% per year.  What will Bryson's car be worth in 4 years?

What is $10440.13?

300

You are going to invest some money in a mutual fund next week.  The interest will be compounded monthly at a rate of 8.5%.  When you retire in 2061, you want to receive $185,000.  How much will you need to invest?

What is $6248.50?

400

You invest $2000 at an interest rate of 6% compounded continuously.  How long will it take you to double your money?

What is 11.55 years?

500

A city's population is 200,000.  If it grows by 12% every year, how long will it take the city's population to triple?

What is 9.7 years?

Changing Forms

100

Rewrite in rational exponential notation:

sqrt(x^3)

What is 

x^(3/2)

200

Rewrite in radical notation:

x^(5/2)

What is 

sqrt(x^5)

300

Write in exponential form:

log 1000 = 3

What is 

10^3=1000

400

Write in log form:

e^y=x

What is 

ln x = y

500

Rewrite in radical notation:

x^(1/5)

What is 

root(5)x