# Logarithms

The definition of a Logarithm, or Log, is that it is the inverse of an exponential function. This is probably of little help, so a simplified description follows.

Take a multiplication of 10 x 10 = 100
This is known as 10 to the power of 2, or 102
If the power is increased the results are:
• 10^2 = 10 x 10 = 100
• 10^3 = 10 x 10 x 10 = 1,000
• 10^4 = 10 x 10 x 10 x 10 = 10,000

A Log is the inverse of this, so the Log of 100 = 2
Repeating the numbers above in logarithmic form:
• Log10 100 = 2  (Log10 as numbers are decimal)
• Log10 1,000 = 3
• Log10 10,000 = 4
So normal multiplication: 10 x 10 = 100
Can be rewritten as:        Log10 1 + Log10 1 = Log10 2

This means that multiplication can be done by adding Logs instead. This was very useful in the days before calculators when Log Tables and Slide Rules were used to calculate. A second use is when working with numbers that increase in an accelerated form, such as the human eye response to light intensity.  If the numbers increase exponentially (1, 10, 100, 1000...) then it is more efficient to use Logs as they increase linearly (0, 1, 2, 3...) instead. Finally, since digital imaging uses binary rather than decimal numbers, the Logs need to be based on 2 instead of 10.  As a result the value of the Log numbers change.
• Decimal:   Log number 2 = 100    (Log10 100 = 2)
• Binary:    Log number 2 = 4      (Log2 4 = 2)
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