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A logarithm is an
exponent.
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In the example shown above, 3 is the
exponent to which the
base 2 must be raised to create the answer
of 8, or 23
= 8. In
this example, 8 is called the
anitlogarithm base
2 of 3.
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Try to remember the "spiral"
relationship between the values as shown at the right.
Follow the arrows starting with base 2 to get the
equivalent exponential form.
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In general terms:
(where x > 0 and
b is a positive constant
not equal to 1) |
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Logarithms with base 10 are called
common logarithms.
When the base is not indicated, base 10 is implied.
Logarithms with base e
are called natural logarithms.
Natural logarithms are denoted by ln.
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e
2.71828183 |
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On the graphing calculator: |
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The base 10
logarithm is the log key.
The base e logarithm is the ln key.
To enter
a logarithm with a different base,
use the Change of Base
Formula:
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Properties of Logs:
Using
the properties of exponents, we
can arrive at the properties of
logarithms. |
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Properties of
Exponents:
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Let's see
the connection:
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Similar investigations
lead to the other
logarithmic properties. |
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Also:
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These log
properties remain the same when
working with the natural log:
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| Remember: ln 1
= 0 and ln
e = 1 |
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Examples:
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