/JavaScript

# Math.log1p()

The Math.log1p() static method returns the natural logarithm (base e) of 1 + x, where x is the argument. That is:

$β x > β 1 , πΌπππ.ππππ·π ( π‘ ) = ln ( 1 + x ) \forall x > -1,;\mathtt{\operatorname{Math.log1p}(x)} = \ln(1 + x)$

## Syntax

js
Math.log1p(x)


### Parameters

x

A number greater than or equal to -1.

### Return value

The natural logarithm (base e) of x + 1. If x is -1, returns -Infinity. If x < -1, returns NaN.

## Description

For very small values of x, adding 1 can reduce or eliminate precision. The double floats used in JS give you about 15 digits of precision. 1 + 1e-15 = 1.000000000000001, but 1 + 1e-16 = 1.000000000000000 and therefore exactly 1.0 in that arithmetic, because digits past 15 are rounded off.

When you calculate log(1 + x) where x is a small positive number, you should get an answer very close to x, because $lim x β 0 log β‘ ( 1 + x ) x = 1 \lim_{x \to 0} \frac{\log(1+x)}{x} = 1$. If you calculate Math.log(1 + 1.1111111111e-15), you should get an answer close to 1.1111111111e-15. Instead, you will end up taking the logarithm of 1.00000000000000111022 (the roundoff is in binary, so sometimes it gets ugly), and get the answer 1.11022β¦e-15, with only 3 correct digits. If, instead, you calculate Math.log1p(1.1111111111e-15), you will get a much more accurate answer 1.1111111110999995e-15, with 15 correct digits of precision (actually 16 in this case).

If the value of x is less than -1, the return value is always NaN.

Because log1p() is a static method of Math, you always use it as Math.log1p(), rather than as a method of a Math object you created (Math is not a constructor).

## Examples

### Using Math.log1p()

js
Math.log1p(-2); // NaN
Math.log1p(-1); // -Infinity
Math.log1p(-0); // -0
Math.log1p(0); // 0
Math.log1p(1); // 0.6931471805599453
Math.log1p(Infinity); // Infinity


## Browser compatibility

Desktop Mobile Server
Chrome Edge Firefox Opera Safari Chrome Android Firefox for Android Opera Android Safari on IOS Samsung Internet WebView Android Deno Node.js
log1p 38 12 25 25 8 38 25 25 8 3.0 38 1.0 0.12.0