Logarithm

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Logarithms or logs are a part of mathematics. A log is the inverse (opposite) of exponentiation; this is, it tells what exponent (power) is needed to make a certain number. So since

$2^3= 2 \times 2 \times 2=8$ ,

the logarithm to a base 2 of 8 is 3, written as:

$\log_2(8) = 3\$

Logarithms to base 10 are known as common logs and are usually written without the base; for example:

$\log(100) = 2\$ because $10^2 = 100\$

$\log(25.6) = 1.4082\$ because 10^(1.4082) = 25.6

Seeing that 10^1.41 = 25.704 and even 10^1.408 = 25.585, you might notice that it's important to keep at least four digits in the mantissa (the part of the number that follows the decimal on a logarithm) if precision is important.

[change] Common bases for logarithms

base	abbreviation	Comments
2	$lg$	Very common in Computer Science
e	$ln$	The base of this is the Eulerian constant e, which is 2.718...
10	$log$
any other number, n	$log n$	This is the general way to write logarithms