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# Math.log

## Math.log

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

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

## Syntax

Math.log(x)

### Parameters

x
A number.

## 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).

## 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. $\log_x y$):

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.