Logs Unit

Exponential and Logarithmic forms

100

10³=1,000

log(1000)=3

200

12²=144

log₁₂(144)=2

300

15²=225

log₁₅(225)=2

400

64^1/3=4

log₆₄(4)=1/3

500

(x-1)²=x²-2x+1

log_(x-1)(x²-2x+1)=2

Logarithmic equations

100

log₅2

0.431

200

log₂5

.322

300

log₃10

2.096

400

log₄1048

5.5

500

log₇2.5

0.471

Condense logarithms

100

log₃(ab)

log₃a+log₃b

200

log₄(ab²)

log₄a+2log₄b

300

log₅(3ab)²

log₅9+2log₅a+2log₅b

400

Log₇(a²b³)⁵

log₇a+15log₇b

500

log a+log b

log(a⁴b⁴)

Exponential equations that require logs

100

2^x=3

x=1.585

200

4^x=19

x=2.124

300

8+10^2x=1008

x=1.5

400

12^x+1=36

x=0.358

500

4^x-1=4^2x

x=-1

Word Problems

100

Barthalomew bought a truck for $22,305, but it has depreciated at a rate of 8.5% since he bought it. If its not worth $14,334.51, how long has he owned the truck?

5 years

200

A virus is spreading at a rate of 4.5% per day. Currently there are 300 people infected, about how long will it take for there to be 1000 people infected?

28 days

300

The local gym currently has 100 members. The membership enrollment is increasing at a rate of 8% per year. To the nearest whole number, how many members will the local gym have in 5 years?

147 members

400

The world population in 2000 was approximately 6.08 billion. The annual rate of increase was about 1.26%. Write a function to model world population growth since 2000. Predict the population in the year 2040.

10.06 Billion

500

A population of bacteria is modeled by the equation N=50x3^t, Where t is time in hours.

How long will it take for the population to reach 1,350

3 hours/t=3