November 18, 2009
November 18, 2009
November 18, 2009
3.3 Logarithmic Functions
y=bx
x
Does the function: y = b have an
inverse?
What does it look like?
domain:
range:
The inverse of an exponential function f(x)=bx is a
logarithmic function with base b
y = logbx iff
by = x
November 18, 2009
Given an equ. in exp. form, write it in log form.
Exp. Form
1. 23=8
2. 102=100
3. 4-2=
1
16
4. 34=81
Log. Form
November 18, 2009
Properties:
logb1 = 0
because b0 = 1
log b = 1
b
because b1 = b
logbby = y
because by = by
b
logbx
=x
because log x = log x
b
b
November 18, 2009
Evaluate.
1. log2128
2. log.2125
3. log3x=4
4. logx 1 -4
81
5. log127 = x
3
November 18, 2009
common logs
base 10
natural logs
base e
y = log x iff
y = ln x
10y = x
iff ey =x
November 18, 2009
Evaluate.
1. log 100
2. log 10
3. log
4. 10
1
1000
log6
November 18, 2009
Evaluate.
1. ln 4
2. ln e2
3. ln 1
e2
4. ln (-1)
November 18, 2009
Solve.
1. log x = 5
2. ln x = -3
November 18, 2009
Transformations
1. g(x) = log10(x-1)
2. h(x) = 2 + log10x