Exponentials and Logarithms (7.4-7.6)

Properties of Logs

100

Which property would you use to combine these logs?

log100 - log10

Quotient

200

Which property would you use to combine these logs?

log₂5 + log₂4

Product

300

Which property of logs would you use first to combine these logs?

2log₄x - log₄y

Power

400

Evaluate the following and identify the rule used. (round to the nearest hundredth)

log_3(5)

1.46

Change of base formula

Expand logs

100

Expand the log expression 

log₃6²

2log₃6

200

Expand the log expression 

log_5(2/x)^4

4log_5(2)-4log_5(x)

300

Expand the log expression 

log_9((x^2)/(2y^3))

2log_9(x)-log_9(2)-3log_9(y)

400

Expand the log expression 

logsqrt(x^3y^5)

3/2logx+5/2logy

Condense Logs

100

Condense the following logs

log_2(10)-log_2(5)

log_2(2)=1

200

Condense the following logs

3log_3(x)-2log_3(y)

log_3(x^3/y^2)

300

Condense the following logs

2log3-log3-4logx

log(3/x^4)

400

Condense the following logs

1/3log_4(8)-5log_4(2)

log_4(1/16)

Exponential Equations

100

Solve for x. Round to the nearest hundredth.

2^x=20

x=4.32

200

Solve for x. Give the exact answer.

3^(x-2)=9

x = 4

300

Solve for x. Round to the nearest hundredth.

e^(2x+3)=5

x = -0.70

400

The population of lionfish in the waters surrounding Florida can be measured using the equation below where x is the number of years and y is the population in thousands? About how many years will it take for the population to reach 400,000?

y=250(1.04)^x

12 years

500

You invest $100 into an account with an annual interest rate of 5.5% with continuous compounding. How long will it take for your investment to triple?

Hint: What is the equation you want to use?

A = Pe^(rt)

300 = 100e^(0.055r)

r ≈ 20 years

Log equations

100

Solve for x

log_4(x)+log_4(2)=3

x=32

200

Solve for x

3log_2(x)-log_2(4)=log_2(16)

x = 4

300

Solve for x. Round to the nearest hundredth.

ln(x+2)-ln4=3

x = 78.34

400

Solve for x. 

log_9(x)+log_9(x-6)=1

No solutions

E.S. -3