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A logarithm is an exponent.
In the example shown at the right, 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 antilogarithm 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, 23 = 8. |
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A logarithm base b of a positive number x is such that:
for b > 0, b≠ 1, logb x = y if and only if by = x.
The log bx is read "log base b of x".
The logarithm y is the exponent to which b must be raised to get x. |
Logarithms with base 10 are called common logarithms. When the base is not indicated, base 10 is implied.
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Logarithms with base e are called
natural logarithms. Natural logarithms
are
denoted by ln.
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Logarithms with base 10 are called common logarithms and are written without the 10 showing.
The log key will calculate common
(base 10) logarithms. |
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Logarithms with the base e are called natural logarithms and are written using the notation ln( x).
The ln key will calculate natural
(base e) logarithms. |
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For " other bases" use the change of base formula:
is entered as
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Origins of Change of Base Formula:
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Set = x. |
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Convert to exponential form. |
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Take common log of both sides. |
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User power rule. |
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Divide by log b. |
Change of Base Formula: |
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The logBASE( operation template can also be used.
To load the template go to
MATH → arrow down to A: logBASE(.
For more options, see link below:
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For more help with logarithms on your calculator, click here.
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Examples:
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