Logarithms Review (AA2)

Evaluating Logs

100

log₂8=

3

200

log₆₄8

1/2

300

log₄(1/2)

-1/2

400

log₈₁27

3/4

500

log₁₆(1/64)

-3/2

Log Properties

100

Condense into one log: log x - 2 log y

log(x/y²)

200

Expand completely: log₂(xy²/z)

log₂x + 2log₂y - log₂z

300

Condense into one log: 2(ln3 + ln4) - ln9

ln16

400

Given: log₃4=1.3, log₃5=1.5, and log₃2=0.6, calculate log₃400

5.6

500

Given: log₃4=1.3, log₃5=1.5, and log₃2=0.6, calculate log₃200

4.9

Solving Exponentials

100

Solve: 2^x+1=2^2x-3

4

200

Solve: 5^-3x=625

-4/3

300

Solve (answer exact): 11^7x+5=105

(log₁₁100)/7

400

Solve (answer exact): 7e^x-4-6=53

(log₁₁100)/7

500

Solve (answer exact): -9*5^-4x-2-1=-3

(-log₅(2/9) - 2)/4

Solving Logarithms

100

Solve (answer exact): log₂(3r+4)=log₂(-5r+2)

-1/4

200

Solve (answer exact): 8+log₂10x=12

8/5

300

Solve (answer exact): 3log₈(x-4)+4=1

33/8

400

Solve (answer exact): log₈(-4x)-log₈9=log₈22

-99/2

500

Solve (answer exact): log₇3x-log₇3=1

7

Word Problems

100

A national park has a population of 5000 deer in the year 2016. Conservationists are concerned because the deer population is decreasing at the rate of 7% per year. If the population continues to decrease at this rate, how long will it take until the population is only 3000 deer?

(log(3/5))/(log0.93) or (ln(3/5))/(ln0.93)

200

A video posted on YouTube initially had 80 views as soon as it was posted. The total number of views to date has been increasing exponentially according to the exponential growth function y=80e^0.2t, where t represents time measured in days since the video was posted. How many days does it take until 2500 people have viewed this video?

(ln(250/8))/0.12

300

A fact sheet on caffeine dependence from Johns Hopkins Medical Center states that the half life of caffeine in the body is between 4 and 6 hours. Assuming that the typical half life of caffeine in the body is 5 hours for the average person and that a typical cup of coffee has 120 mg of caffeine. How long does it take until only 20 mg of caffeine is still in the body?

(5log(1/6))/(log(1/2))

400

Suppose that Vinh invests $10000 in an investment earning 5% per year. He wants to know how long it would take his investment to accumulate to $12000 if the interest is compounded monthly. 

log(6/5)/(12log(1+0.05/12))

500

Suppose that Vinh invests $10000 in an investment and after 5 years he has a total of $12000. What was the rate if it was compounded continuously.

ln(6/5)/5