# JavaScript Math log()

The JavaScript Math.log() function returns the natural logarithm of a number.

It returns the natural logarithm (base e) of a number. It is equivalent to `ln(x)` in mathematics.

The syntax of the `Math.log()` function is:

``Math.log(x)``

`log()`, being a static method, is called using the `Math` class name.

## Math.log() Parameters

The `Math.log()` function takes in:

• x - A number

## Return value from Math.log()

• Returns the natural logarithm (base e) of the given number.
• Returns `NaN` for negative numbers and non-numeric arguments.

## Example 1: Using Math.log()

``````// Using Math.log()
var value = Math.log(1);
console.log(value); // 0

var value = Math.log(Math.E);
console.log(value); // 1

var value = Math.log("10");
console.log(value); // 2.302585092994046

var value = Math.log(0);
console.log(value); // -Infinity

var value = Math.log(-1);
console.log(value); // NaN``````

Output

```0
1
2.302585092994046
-Infinity
NaN```

## Example 2: Using Math.log() for other bases

The numerical value for logarithm to any base `a` from any base `b` can be calculated with the following change of base identity:

`loga(N) = logb(N) / logb(a)`

So, we can use `Math.log()` to calculate the logarithm in any base in the following way:

``````// find logarithm in any base

function log(base, number) {
return Math.log(number) / Math.log(base);
}

// calculating log(100) in base 10
var value = log(10, 100);
console.log(value); // 2

// calculating log(10) in base 5
value = log(5, 10);
console.log(value); // 1.4306765580733933``````

Output

```2
1.4306765580733933```

Notes:

• Use the constants `Math.LN2` or `Math.LN10` for natural log of 2 and 10 respectively.
• Use the functions `Math.log2()` or `Math.log10()` for logarithm base 2 and 10.