Properties of Logs
Expand the following: log (x2yz4)
2log x + log y + 4 log z
Growth or Decay: y= 200(.5)x
Decay
Write in exponential form: log3(9)=2
32=9
Solve: 2x=8
x= 3
The amount of money in a savings account t, years after it has been opened is given by P(t)=11000(1.025)t. How many years will it take for the amount in the account to reach $14433?
t =11 years
Expand the following: log (x/y6)
log x - 6log y
Growth or Decay: y=2(1.5)x
Growth
Write in exponential form: log5(1/25)=-2
5-2=1/25
Solve: 3 * (4x) = 39
x= 1.85
If a home is currently valued at $188,000 appreciates at a rate of 3% per year, how many years will it take to reach $292,897.87?
t= 15 years
Write the expression as a single logarithm:
3 log x - log y
log (x3/y)
25%
Write in log form: 27=128
log2(128)=7
Solve: 100 = 5 * 3x
x = 2.73
If a person currently making $53,000 per year receives annual raises of 4.3% per year, how long will it take for the salary to reach $100,000?
t = 15 years
Write the expression as a single logarithm:
5log x - 2 log y + log z
log (x5/y2z)
Find the growth rate: y=5(1.2)x
20%
Write in log form: 6-2=1/36
log6(1/36)=-2
Solve: 2 * (10x) = 1000
x = 2.7
A savings account is started with $40,000. After t years the amount in the account is given by P(t)=40,000e0.04t. How many years will it take for the amount in this account to double?
t = 17 years
Expand the following: log (x/yz)
log x - log y + log z
Find the y-intercept: y=5(.6)x
(0,5)
2.904
Solve: log (3x -2) =2
34
If the population of one city is 77000 and it is growing at a rate of 2.2% per year, and the population of another city is 52000 and is growing at a rate of 4.5%, how long will it take for the two cities to have the same population?