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# JavaScript - Math.log() method example

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

``````// ONLINE-RUNNER:browser;

// Natural logarithm (logarithm with base e):
//                     x            y
console.log( Math.log( 1    ) ); // 0
console.log( Math.log( 7    ) ); // 1.9459101490553132
console.log( Math.log( 10   ) ); // 2.3025850929940460
console.log( Math.log( 100  ) ); // 4.6051701859880920
console.log( Math.log( 1000 ) ); // 6.9077552789821370

console.log( Math.log( -1        ) ); //  NaN
console.log( Math.log(  0        ) ); // -Infinity
console.log( Math.log( +Infinity ) ); // +Infinity

console.log( Math.E ); // 2.718281828459045

// Logarithm with custom base is placed in below example.``````

The `Math.log()` method is presented on the following chart:

## 1. Documentation

 Syntax `Math.log(x)` Parameters `x` - integer or float number value in range `0` to `+Infinitive` (primitive value). Result `number` value calcualted as ln(x) mathematical function (primitive value). If `x` is nagative it returns `NaN`. If `x` is equal to `0` it returns `-Infinity`. If `x` is equal to `+Infinity` it returns `-Infinity`. Description `log` is a static method that takes one parameter and returns an approximation of the ln(x) function (natural logarithm function - logarithm with base `e`).

## 2. Logarithm with custom base example

This example shows a logarithmic function calculation with own base.

``````// ONLINE-RUNNER:browser;

function calculateLogarithm(base, x) {
var a = Math.log(x);
var b = Math.log(base);

return a / b;
}

// Logarithm with custom base:
//                               base    x               y
console.log( calculateLogarithm( 2,      2      ) ); //  1
console.log( calculateLogarithm( 2,      4      ) ); //  2
console.log( calculateLogarithm( Math.E, Math.E ) ); //  1
console.log( calculateLogarithm( 3,      9      ) ); // ~2
console.log( calculateLogarithm( 3,      81     ) ); // ~4
console.log( calculateLogarithm( 10,     10     ) ); //  1``````

## 3. Canvas plot example

``````// ONLINE-RUNNER:browser;

<!doctype html>
<html>
<style> #canvas { border: 1px solid black; } </style>
<body>
<canvas id="canvas" width="400" height="400"></canvas>
<script>

var canvas = document.querySelector('#canvas');
var context = canvas.getContext('2d');

// logarithm chart range
var x1 =  0;
var x2 = 10;
var y1 = -5;
var y2 =  4;

var dx = 0.005;

var xRange = x2 - x1;
var yRange = y2 - y1;

function calculateLogarithm(base, x) {
var a = Math.log(x);
var b = Math.log(base);

return a / b;
}

function calculatePoint(base, x) {
var y = calculateLogarithm(base, x);

// chart will be reversed horizontaly because of reversed canvas pixels

var nx = (x - x1) / xRange;       // normalized x
var ny = 1.0 - (y - y1) / yRange; // normalized y

var point = {
x: nx * canvas.width,
y: ny * canvas.height
};

return point;
}

function drawChart(base, color, thickness) {
var point = calculatePoint(base, x1);

context.beginPath();
context.lineWidth = thickness;
context.strokeStyle = color;
context.moveTo(point.x, point.y);

for (var x = x1 + dx; x < x2; x += dx) {
point = calculatePoint(base, x);
context.lineTo(point.x, point.y);
}

point = calculatePoint(base, x2);
context.lineTo(point.x, point.y);
context.stroke();
}

console.log('log_2(x)  <- red');
console.log('log_e(x)  <- green');
console.log('log_10(x) <- blue');

//           base     color   thickness
drawChart(      2, '#ff001b',       0.8 ); // red
drawChart( Math.E, '#159600',       2   ); // green
drawChart(     10, '#0000ff',       0.8 ); // blue

console.log('x range: <' + x1 + '; ' + x2 + '>');
console.log('y range: <' + y1 + '; ' + y2 + '>');

</script>
</body>
</html>``````

## References

1. Natural logarithm - Wikipedia