Unit 7: Exponential and Log Review

Conversions

100

Convert to an exponential:

log₁₁x=2

11²=x

200

Convert to an exponential

log15=x

10^x=15

300

Convert to an exponential

lnx=30

e³⁰=x

400

Convert to a log

x^y=178

log_x178=y

500

Convert to a log

b⁷=109

log_b109=7

Condense/Expand

100

Condense

log2+4logx

log(2x⁴)

200

Condense

logx+logy+6logz

log(xyz⁶)

300

Condense 

2logx + 12logy- logz

log((x^2y^12)/z)

400

Expand

log((x^3 7^x)/y)

3logx +xlog7 - logy

500

Expand

log(z^(1/2)/(xy))

1/2logz -logx -logy

Solve

100

Solve for x:

log(4x-5)=log(2x-1)

x = 2

200

Solve for x:

log(5x-20)=2

x = 24

300

Use log properties to condense, then solve for x:

log₂(4x+1)-log₂(3)=5

 x = 

95/4

400

Solve for x:

log₂(x+2) - log₂(x-5) = 3

x = 6

500

Solve for x:

log₂x + log₂(x-2) = 3

x = 4

Exponential Word Problems

100

A town with a population of 5,000 grows 3% per year. Find the population at the end of 10 years.

About 6719

200

Amy makes an initial investment of $5000. The investment loses 13.5% each year. Find the amount Amy has at the end of 8 years

About $1567.11

300

A population of 800 beetles is growing each month at a rate of 5%. How long will it take for the population to double?

About 14.2 months 

400

 A radioactive element decays at a rate of 5% annually. There are 40 grams of the substance present. After how many years will half of the substance remain.

About 13.5 years

500

The initial height of a ball is 120 inches, each bounces height decreased by 25%. How many bounces will it take for the height to reach about 0.9inches

About 25 bounces.