# Math.log()

The ** Math.log()** function returns the natural logarithm (base

`e`

) of a number, that is$$\backslash forall\; x\; >\; 0,\; \backslash mathtt\{\backslash operatorname\{Math.log\}(x)\}\; =\; \backslash ln(x)\; =\; \backslash text\{the\; unique\}\; \backslash ;\; y\; \backslash ;\; \backslash text\{such\; that\}\; \backslash ;\; e^y\; =\; x$$

## 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. $\backslash log\_x\; y$):

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 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) |

## See also

## License

© 2016 Mozilla Contributors

Licensed under the Creative Commons Attribution-ShareAlike License v2.5 or later.

https://developer.mozilla.org/en-us/docs/web/javascript/reference/global_objects/math/log