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Logarithms or Logs are a simple way of performing complex calculations in a very simple manner without much effort. The concept of Logarithms was invented by John Napier and Joost Burgi in the early 17th century. Logarithm tables were used to perform calculations until electronic calculators were invented.
A logarithm of a number is given base is the power to which the base must be raised in order to produce that number.
For example, the logarithm of 10000 with base 10 is 4. This is because 10 to the power of 4 is 10000.
The logarithm of x to the base b is written as logb(x), such as log10(10000) = 4.
Logarithms reduce products to sums: Logb(xy) = logb(x) + logb(y)
Powers to Products: Logb(xp) = p logbx
Division to Subtraction : Logb(x÷y) = logb(x) – logb(y)
The Logarithm of the p-th root of a number is the logarithm of that number divided by p: Logb(p√x) = logbx∕p.
Examples
- Log2(32) = log2 4 + log2 8 = 2 + 3 = 5
- Log48 + log4 32 = log4(8)(32) = log4(256) = 4
- Log3 162 – log32 = log3(162/3) = log3 (81) =4
- Log2 (410) = 10 log2(4) = 10(2) = 20
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