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

x>0,Math.log(x)=ln(x)=the uniqueysuch thatey=x\forall x > 0, \mathtt{\operatorname{Math.log}(x)} = \ln(x) = \text{the unique} \; y \; \text{such that} \; e^y = x

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 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. logxy\log_x y):

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 Status Comment
ECMAScript 1st Edition (ECMA-262) Standard Initial definition. Implemented in JavaScript 1.0.
ECMAScript 5.1 (ECMA-262)
The definition of 'Math.log' in that specification.
Standard  
ECMAScript 2015 (6th Edition, ECMA-262)
The definition of 'Math.log' in that specification.
Standard  
ECMAScript Latest Draft (ECMA-262)
The definition of 'Math.log' in that specification.
Draft  

Browser compatibility

Update compatibility data on GitHub
DesktopMobileServer
ChromeEdgeFirefoxInternet ExplorerOperaSafariAndroid webviewChrome for AndroidEdge MobileFirefox for AndroidOpera for AndroidSafari on iOSSamsung InternetNode.js
Basic supportChrome Full support YesEdge Full support YesFirefox Full support 1IE Full support YesOpera Full support YesSafari Full support YesWebView Android Full support YesChrome Android Full support YesEdge Mobile Full support YesFirefox Android Full support 4Opera Android Full support YesSafari iOS Full support YesSamsung Internet Android Full support Yesnodejs Full support Yes

Legend

Full support  
Full support

See also

Document Tags and Contributors

Last updated by: wbamberg,