10_2notes_291.notebook
Warm­up!
f(x) = 3x + 1;
Find 1. 2.
3. Find the inverse.
y = 2x ­ 3
y = 2x April 22, 2016
10­2 Logarithms and Logarithmic Functions
logarithm was invented by John Napier in 1614
Does this graph have an inverse?
The inverse of y = 2x is x = 2y.
Does this graph have an inverse?
x = 2y is commonly expressed as y = log2x
(graph both on Desmos)
Inverses of each other
y = bx y = logbx
What is the inverse?
y = 10x
1
10_2notes_291.notebook
April 22, 2016
Characteristics of a Logarithmic Function
Suppose b and x are positive, and b ≠ 1, then, there is a number y such that:
logbx = y iff by = x (Used to convert between logarithmic and exponential form.)
logbx = y iff by = x logbx = y iff by = x Logarithmic Form
Logarithmic Form
Exponential Form
Exponential Form
log101000 = 3
log216 = 4
log164 = .5
log28 = 3
log327 =3
log21 = 0
log981 = 2
log2x = y
logbx = y
Evaluate a logarithmic expression.
ex
log264
ex
log255
ex
log100.1
Remember:
Two functions are inverses iff
[f g] x = x and [g f] x = x
Inverses of each other
y = bx y = logbx
f(x) = bx g(x) = logbx
Properties of logs
logbbx = x
2
10_2notes_291.notebook
April 22, 2016
DO:
1. log 32 ½
ex
log225
ex
log442
ex
log749
2. log927
3. log5125
ex
ex
4. log84
9
5. 9log 5
6. p536
21­31odd
33­44
3