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Logarithms, often known as logs, are a straightforward method of carrying out intricate computations with minimal effort. Early in the 17th century, John Napier and Joost Burgi came up with the idea of logarithms. Before the invention of electronic calculators, computations were done using logarithm tables.

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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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