Log Functions
Properties of Logs
Common/Natural Logs
Computing or Solving
Potpourri
100
The exponential form of this is what?
100
Condense:
log 6 + log y - log z
log 6y/z
100
This number is the base of the Natural Logarithm
What is e or Euler's number
100
Evaluate without a calculator:
1
100
Describe the transformations:
f(x) = log4(x - 3) + 4
3 right and 4 up
200
The one word description of a logarithm
A logarithm is an exponent
200
Expand: log2A4B6
4log2A+6log2B
200
log x, what is the base?
10
200
Evaluate without a calculator:
0
200
Liam wants to have $10,000 in a savings account 5 years from now. The account offers an annual interest rate of 5%, compounded monthly.
How much money does he need to deposit now (the principal) to reach his goal?
P(1 + .05/12)60 = 10,000
P = $7792
300
A logarithmic function is the inverse of these functions.
What are Exponential Functions
300
This can be written as a single logarithm
What is:
300
Mrs. Prime deposited $60 into an account that is continuously compounded at a rate of 3.25%. How much money will she have in 10 years?
60e.0325(10)
$83.04
300
Solve for x: 2(7)x - 5 = 17
7x = 11
log711 = x, log 11/log 7 = 1.23
300
Write the exponential function that contains the points (3,16) and (6,1024).
f(x) = .25(4)x
400
Express in log form: 9x=50
What is log950=x
400
Condense:
1/2(ln x - ln y) + 3ln z
ln (x/y)1/2z3
400
What is the value of (no calculator):
What is 1/3
400
Solve for x. Check for extraneous solutions:
2log x - log 5 = log 4
log x2/5 = log 4
x2/5 = 4
x2 = 20
x = plus or minus 2root5, negative 2root5 is extraneous
400
f(x) = 3(2)x + 5 - 4
Identify the domain, range, and equation for the asymptote.
Domain: all real #
Range: y > -4
Asymptote: y = -4
500
Express in exponential form: log5x=4
What is 54=x
500
Solve for x. Check for extraneous solutions.
log 2x + log 5 = 2
log 10x = 2
102 = 10x
100 = 10x
10 = x
500
How long will it take my money to triple if I deposited $100 at a 5.1% interest rate that is compounded continuously?
300 = 100e.051t
3 = e.051t --> ln 3 = .051t
t = ln 3 / .051
t = 21.5 yrs
500
Solve for x. Check for extraneous solutions:
log x + log (x - 3) = 1
log (x2 - 3x) = 1
101 = x2 - 3x
0 = x2 - 3x - 10
0 = (x - 5)(x + 2), x = 5, -2, -2 is extraneous
500
Identify the domain, range, and asymptote:
f(x) = -log2(x + 4) - 1
Domain: x > -4
Range: all real #
Asymptote: x = -4