# Math.log()

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

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

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 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).

Beware that positive numbers very close to 1 can suffer from loss of precision and make its natural logarithm less accurate. In this case, you may want to use Math.log1p instead.

## 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 (i.e. $\log_x y$):

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
ECMAScript Language Specification
# sec-math.log

## Browser compatibility

BCD tables only load in the browser