Logarithm Calculator (Any Base)

Enter a number and a base to compute log_b(x). It also shows the natural log ln, common log log10, and binary log log2, with a curve graph.

Input

Enter the number x (greater than 0) and the base b (greater than 0 and not 1) to compute the logarithm log_b(x).

Number x

A positive number greater than 0

Base b

Greater than 0 and not equal to 1

Result

log base 2

Change of base

log_b(8) = ln(8) ÷ ln(2)

Natural log ln (base e)

2.07944154

Common log log10

0.90308999

Binary log log2

A logarithm with any base is found by the change of base formula log_b(x) = ln(x) divided by ln(b). The number must be positive and the base must be a positive value other than 1.

How it works

The logarithm log_b(x) is the exponent to which the base b must be raised to produce the number x. For example log_2(8) equals 3 because 2 raised to the power 3 is 8.
A logarithm with any base is computed from the change of base formula log_b(x) = ln(x) divided by ln(b). This tool uses that formula.
The number x must be greater than 0. Real logarithms are undefined for values that are 0 or negative.
The base b must be greater than 0 and not equal to 1. When the base is 1 the divisor ln(b) becomes 0 and the result is undefined.
The natural log ln uses base e (about 2.71828), the common log log10 uses base 10, and the binary log log2 uses base 2.

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