# Math.log()

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

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

## Syntax

JavaScript
Math.log(<var>x</var>)

### 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()

JavaScript
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. $\log_x y$):

JavaScript
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 2017 Draft (ECMA-262)
The definition of 'Math.log' in that specification.
Draft

## Browser compatibility

Feature Chrome Firefox (Gecko) Internet Explorer Opera Safari
Basic support (Yes) (Yes) (Yes) (Yes) (Yes)
Feature Android Chrome for Android Firefox Mobile (Gecko) IE Mobile Opera Mobile Safari Mobile
Basic support (Yes) (Yes) (Yes) (Yes) (Yes) (Yes)