
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 2^{3} = 8.
In this example, 8 is called the antilogarithm base 2 of 3. 

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, 2^{3} = 8. 

A logarithm base b of a positive number x is such that:
for b > 0, b≠ 1, log_{b }x = y if and only if b^{y} = x.
The log b^{x} 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.

Logarithms with base e are called
natural logarithms. Natural logarithms
are
denoted by ln.


Logarithms with base 10 are called common logarithms and are written without the 10 showing.
The log key will calculate common
(base 10) logarithms. 

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. 


For " other bases" use the change of base formula:
is entered as


Origins of Change of Base Formula:

Set = x. 

Convert to exponential form. 

Take common log of both sides. 

User power rule. 

Divide by log b. 
Change of Base Formula: 



For help with logarithms on your calculator, click here.



Examples:
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