files/en-us/web/javascript/reference/global_objects/math/log/index.md

metadata

title: Math.log()
short-title: log()
slug: Web/JavaScript/Reference/Global_Objects/Math/log
page-type: javascript-static-method
browser-compat: javascript.builtins.Math.log
sidebar: jsref

The Math.log() static method returns the natural logarithm (base e) of a number. That is

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

{{InteractiveExample("JavaScript Demo: Math.log()")}}

function getBaseLog(x, y) {
  return Math.log(y) / Math.log(x);
}

// 2 x 2 x 2 = 8
console.log(getBaseLog(2, 8));
// Expected output: 3

// 5 x 5 x 5 x 5 = 625
console.log(getBaseLog(5, 625));
// Expected output: 4

Syntax

Math.log(x)

Parameters

• x
  • : A number greater than or equal to 0.

Return value

The natural logarithm (base e) of x. If x is ±0, returns -Infinity. If x < 0, returns {{jsxref("NaN")}}.

Description

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 {{jsxref("Math.LN2")}} or {{jsxref("Math.LN10")}}. If you need a logarithm to base 2 or 10, use {{jsxref("Math.log2()")}} or {{jsxref("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) since multiplication in Math.log(x) * constant is much faster.

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 {{jsxref("Math.log1p")}} instead.

Examples

Using Math.log()

Math.log(-1); // NaN
Math.log(-0); // -Infinity
Math.log(0); // -Infinity
Math.log(1); // 0
Math.log(10); // 2.302585092994046
Math.log(Infinity); // Infinity

Using Math.log() with a different base

The following function returns the logarithm of y with base x (i.e., ${log}_{x}y\backslash log\_x\; y$):

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, but still very close to the actual answer of 3.

Specifications

{{Specifications}}

Browser compatibility

{{Compat}}

See also

• {{jsxref("Math.exp()")}}
• {{jsxref("Math.log1p()")}}
• {{jsxref("Math.log10()")}}
• {{jsxref("Math.log2()")}}
• {{jsxref("Math.pow()")}}