Web/JavaScript/Reference/Global objects/Math/log

The Math.log() function returns the natural logarithm (base e) of a number, that is

<math display="block">\forall x > 0,\mathtt{\operatorname{Math.log}(x)} = \ln(x) = \text{the\ unique}\; y\;\text{such\ that}\; e^{y} = x</math>

The JavaScript Math.log() function is equivalent to ln(x) in mathematics.

Syntax

Math.log(x)

Parameters

x: A number.

Return value

The natural logarithm (base e) of the given number. If the number is negative, NaN is returned.

Description

If the value of x is 0, the return value is always -Infinity.

If the value of x is negative, the return value is always NaN.

Because log() is a static method of Math, you always use it as Math.log(), rather than as a method of a Math object you created (Math is not a constructor).

If you need the natural log of 2 or 10, use the constants Math.LN2 or Math.LN10. If you need a logarithm to base 2 or 10, use Math.log2() or Math.log10(). If you need a logarithm to other bases, use Math.log(x) / Math.log(otherBase) as in the example below; you might want to precalculate 1 / Math.log(otherBase).

Examples

Using Math.log()

Math.log(-1); // NaN, out of range
Math.log(0);  // -Infinity
Math.log(1);  // 0
Math.log(10); // 2.302585092994046

Using Math.log() with a different base

The following function returns the logarithm of y with base x (ie. <math display="inline">\log_{x}y</math>):

function getBaseLog(x, y) {
  return Math.log(y) / Math.log(x);
}

If you run getBaseLog(10, 1000) it returns 2.9999999999999996 due to floating-point rounding, which is very close to the actual answer of 3.

Specifications

Specification
ECMAScript (ECMA-262)The definition of 'Math.log' in that specification.

Browser compatibility

Update compatibility data on GitHub

	Desktop						Mobile						Server
	Chrome	Edge	Firefox	Internet Explorer	Opera	Safari	Android webview	Chrome for Android	Firefox for Android	Opera for Android	Safari on iOS	Samsung Internet	Node.js
`log`	Chrome Full support 1	Edge Full support 12	Firefox Full support 1	IE Full support 3	Opera Full support 3	Safari Full support 1	WebView Android Full support 1	Chrome Android Full support 18	Firefox Android Full support 4	Opera Android Full support 10.1	Safari iOS Full support 1	Samsung Internet Android Full support 1.0	nodejs Full support 0.1.100

Legend

Full support: Full support