Math.log()

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

FeatureChromeFirefoxEdgeInternet ExplorerOperaSafari
Basic Support(Yes)(Yes)(Yes)(Yes)(Yes)(Yes)

See also

Document Tags and Contributors

 Last updated by: fscholz,