# Logarithm Calculator

This online calculator calculates logarithms of a given number with respect to a specific base, as well as the natural logarithm (base e) and the decimal logarithm (base 10) of the number.

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#### Anton

Created: 2010-03-26 20:50:01, Last updated: 2023-02-11 21:30:22

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The user inputs the number and the base, and the calculator outputs the logarithm of the number with respect to the given base, natural logarithm of the number and decimal logarithm of the number.

The logarithm of a number 'x' with respect to a base 'b' is denoted as logb(x) and is calculated as the exponent to which the base 'b' must be raised to equal the number 'x'.

For example, log2(8) = 3 because 23 = 8.

The natural logarithm (base e) of a number 'x' is denoted as ln(x) and is calculated as the logarithm of the number with respect to the mathematical constant 'e' (approximately equal to 2.718).

The decimal logarithm (base 10) of a number 'x' is denoted as log10(x) and is calculated as the logarithm of the number with respect to the base 10.

For example, log10(100) = 2 because 102 = 100.

The following formula is used to get the logarithm with base a provided that you can calculate the logarithm with base c:
$log_a b =\frac{log_c b}{log_c a}$

#### Logarithm

Digits after the decimal point: 3
Logarithm to a given base

Common logarithm

Natural logarithm

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