Math.log()

Baseline Widely available

This feature is well established and works across many devices and browser versions. It’s been available across browsers since July 2015.

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

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

Try it

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)

Return value

The natural logarithm (base e) of x. If x is ±0, returns -Infinity. If x < 0, returns 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 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) 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 Math.log1p instead.

Examples

Using Math.log()

js
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., logxy\log_x y):

js
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

Specification

ECMAScript® 2027 Language Specification
# sec-math.log

Browser compatibility

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This page was last modified on Jul 10, 2025 by MDN contributors.

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Standard built-in objects
Math
Static methods
Static properties
1. E
2. LN2
3. LN10
4. LOG2E
5. LOG10E
6. PI
7. SQRT1_2
8. SQRT2