Logarithms / Exponents Review

Expand/Condense

100

Expand

log_3(x^2/4)

2log_3x-log_3 4

200

Expand

ln(x*y)

ln(x)+ln(y)

300

Condense

log(6)+2log(x)

log(6x^2)

400

Condense

5lnx-(2lny+3lnz)

ln(x^5/(y^2z^3))

500

Condense

eLog_7x^2+pilog_7sqrty

log_7(x^(2e)sqrty^pi)

Evaluate (Round to the ten thousandth)

100

log56

1.7482

200

ln8

2.0794

300

log_8 103

2.2288

400

log_(1/2)5

-2.3219

500

log_sqrt2 81

12.6797

Solve Exponential Equations

100

3^x=50

x=log_3 50 ~~3.5609

200

2^(x+1)-4=5

x=log_2 9-1~~2.1700

300

4e^(-3x)=7

x=(ln(7/4)/-3)~~-.1865

400

3(1/2)^x=6

x=log_(1/2)2=-1

500

1/(2^(-5x))=1/2

x=log_2(2)/5=-1/5=-0.2

Solve Logistic Equations

100

log(5x-1)=log(3x+7)

x=4

200

ln(5)+ln(x^2)=ln(125)

x=+-5

300

ln(x)-ln(8)=2

x=8e^2~~59.1124

400

logx-(log2+log3)=1

x=60

500

DAILY DOUBLE

Inverse Functions

Word Problems

100

A population can be modeled by:

 P(t)=425e^(rt) 

What is the initial population?

425

200

A snail population can be modeled by:

 P(t)=300,000e^(.05t) 

What will be the population in 5 years?

385,208 snails

300

A population can be modeled by:

 P(t)=250e^(.023t) 

How many years will it take to reach a population of 3000?

108 years

400

A population can be modeled by:

 P(t)=a_0e^(.03t) 

If after 45 years the population is 74,000 people, what was the initial population?

19,184 people

500

DAILY DOUBLE

Half-life