November 18, 2013
Introduction to Logarithms
Basic Log function y = logcx
The inverse of an exponential function is a logarithmic function.
Graph:
f(x) = 2x
x
­2
­1
0
1
2
¼
½
1
2
4
y
f(x) = log2x x
y
Characteristics
Domain:
Zero:
Sign:
Variation:
Asymptote: Range: Extrema: November 18, 2013
Graph:
y= (½)x
x
­2
­1
0
1
2
4
2
1
½
¼
y
y = log½x x
y
Characteristics
Domain: Range: Zero: Extrema:
Sign:
Variation:
Asymptote: Note: When c > 1 the function is increasing
When 0 < c < 1 the function is decreasing
November 18, 2013
Definition of a Logarithm
* Remember a logarithm is an exponent!
logcp = q
cq = p Example: log28 = 3 since 23 = 8
base
exponent
• The logarithm in base 10 of a number x is written log x
• The logarithm in base e of a number x is written ln x
Remember: logcx = log x or logcx = ln x
ln c
log c
Example:
log28 = log 8 = 3
log 2
log28 = ln 8 = 3
ln 2
Given: 53 = 125 write in log form
log5125 = 3
Given: log216 = 4 write in exponential form
24 = 16
Evaluate: log 10 =
ln e =
log 1000 = ln e2 = log 0.1 = ln e­1 = log 0.01 = Determine: log2x = 5
x = 25 = 32
logx49 = 2
72 = 49 or √49 = 7
November 18, 2013
Find the rule of the basic log function if it passes through the point (8,3).
Work: Green Book
Pg 183 #1,2
Pg 184 #3­9
Pg 185 # 10­14