Intro to Logarithms
Goes along with 4.4 (GREEN book)
Quiz: 1/12/10
Logs Test: 1/21/10
Introduction
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Logarithms were originally developed to
simplify complex arithmetic calculations.
They were designed to transform
multiplicative processes into additive ones.
If at first this seems like no big deal,
then try multiplying
2,234,459,912 and 3,456,234,459.
(Without a calculator!)
 Clearly, it is a lot easier to add these two
numbers.
Definition
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Logarithms are the "opposite"
of exponentials, just as subtraction is the
opposite of addition and division is the
opposite of multiplication.
Logs "undo" exponentials.
Technically speaking, logs are the inverses
of exponentials.
Lets look at their graphs
y = 10x
y=x
y = log10x
Understanding Logarithms
• The first, and perhaps the most important
step, in understanding logarithms is to realize
that they always relate back to exponential
equations.
• You must be able to convert an exponential
equation into logarithmic form and vice versa.
Exponential
Equation
Logarithmic
Form
103 = 1000
log101000 = 3
Exponent
BASE
(The base of the logarithm must be a positive number other than 1.)
(You can’t take the log of a negative number or zero.)
log xy
y
b =x
Example 1:

Write 53 = 135 in logarithmic form.
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Write log381 = 4 in exponential form.
Try This:
Complete the table.
Exponential
Form
Logarithmic
Form
25 = 32
3-2 = 1/9
log101000 = 3
Log164 = 1/2
Evaluate without a calculator:
1. log 2 8
2. log 2 1
3. Find the value of k :
k = log 9 3
4. Find the value of k :
½ = log k 9
5. Find the value of k :
3 = log 7 k
Common Logarithms
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10 are called
Logarithms with base ______
common logarithms. Sometimes the base is
assumed and not written. Thus, if you see a
log written without a base, you assume the
10
base is _______.
The log button the
10
calculator uses base _____.
Use your calculator to evaluate:
1. log 51
2. log 4
3. log 0.215
4. Solve for x: 10x = 728
5. Solve for x: 10x = 1/1085
Natural Logarithm
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A natural logarithm is a logarithm with base e,
denoted by ln.
A natural logarithm is the inverse of an
exponential function with base e.
Lets look at their graphs
y = ex
y = ln x
y=x
Homework
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Green Book
P. 145 Guided Practice #1-7odd
P. 147 #1-12 all