5.6: Logarithmic Functions
Technology is a way of organizing the universe so
that man doesn't have to experience it.
Think of a
logarithm as
an exponent!
What’s a
logarithm?
Righteous!
Yes; A logarithm is a
another way of
writing exponential
functions!
Graph y  10 and find its inverse.
x
x  10
y
The Inverse Function
1
y  log10 ( x)
1
How the heck
did that
happen?
We need a little more background on logarithms!
Exponential Function
exponent
2 8
3
base
Logarithmic Function
Argument
exponent
log 4 16  2
base
Base to the exponent = the blob
TASTEY!!
!
Special types of Logarithms:
Common Logarithm: A logarithm with base 10.
Ex : 10  1000
3
Log101000 = 3
Natural Logarithm: A logarithm with base e.
12
Ex : e
 1.649
Lne1.649 = 1/2
Now you try some!
Write each exponential equation as a logarithm.
1)
2
4 8
3
Log48 = 3/2
2) 10
2
1

100
Log101/100 = -2
i
3) e  1
Lne-1 = ∏i
Write each logarithmic equation as an exponential.
1) log 4 64  3
2) log 40  1.6
3) ln e  2
43 = 64
101.6 = 40
e2 = e 2
2
Solve. Round decimal answers to the nearest hundredth.
x
x
1) log x 16  4
x-4
2) 10  34
3) 2e  47
ex = 23.5
= 16
Well 2-4 = 1/(2)4 = 1/16,
so then turn it into ½
x=½
Log1034 =x
Lne23.5 = x
Ln 23.5 = 3.157
Check answer
3.157 = 23.4999
e
Log 34 = 1.5315
Check answer
101.531478917 = 34!
Just wait; it
gets even
better!
Dude,
logarithms are
totally cool!
5.6: Logarithmic Functions
Homework: 3 – 31, 40 – 45
Technology is a way of organizing the universe so
that man doesn't have to experience it.