Logarthmic Function
y=ax
For x > 0, a > 0, and a≠1,
y = logax, if and only if x = ay
Sep 17­10:38 AM
Sep 17­10:40 AM
a) log2 32 =
Common Logarithm: a logarithm
function with base 10
b) log42=
Log 10=
c) log31=
Log 1/4=
d) log10 (1/100)=
Sep 17­10:42 AM
Sep 17­10:45 AM
Natural Log: a logarithm
function with base e
Ln e =
Ln 58=
Feb 27­7:26 AM
Feb 27­9:12 AM
1
Properties of Logarithms
a) Solve for x: log2x=log23
1. loga1=0
b) Solve for x: log44=x
2. logaa=1
c) Simplify: log55x
3. logaax=x
d) Simplify: 7log714
4. If logax = logay then x=y
Sep 17­10:47 AM
Properties of the graph of the logarithmic
function come directly from the properties of the graph of
the exponential function and the inverse relationship.
Graphs of Exponential Functions:
Sep 17­10:50 AM
f(x)= log2x
Graphs of Logarithmic Functions:
1) The domain is (­ , ).
1) The domain is (0 , ).
2) The range is (0, ).
2) The range is (­ , ).
3) The y­intercept is (0, 1).
3) The x­intercept is (1, 0).
4) y = 0 is a horizontal asymptote.
5) f is increasing if a > 1.
4) x = 0 is a vertical asymptote.
5) f is increasing if a > 0.
6) f is decreasing if 0 < a < 1
Feb 26­7:07 AM
Graph:
f(x) = log4(x-3)
Sep 17­10:56 AM
Sep 17­10:55 AM
Graph: f(x)= log2(-x)
Sep 18­12:55 PM
2
Graph: h(x) = -log6(x+2)
Sep 18­12:56 PM
Graph: g(x) = log10(x-1) + 4
Sep 18­12:56 PM
Graph: f(x)= log2(-x)
Sep 18­12:55 PM
3