In this tutorial, we will study the MySQL `LOG2()`

and MySQL `LOG10()`

functions. In a previous article, we studied about the MySQL `LN()`

function which finds the natural logarithm (base *e*) of a number.

While studying maths, you must have also come across finding the logarithm to the base 2 or 10 of a number (log_{2 }and log_{10}).

Since these are also widely used logarithmic operations, MySQL provides us with the MySQL `LOG2()`

and `LOG10`

functions.

- The
`LOG2()`

function is used to return the base-2 logarithm of a given number. - The
`LOG10()`

function is used to return the base-10 logarithm of a given number.

Table of Contents

## Syntax of MySQL LOG2()

```
LOG2(number);
```

Where ‘number’ is a numerical value whose base-2 logarithm is to be found out.

## Syntax of MySQL LOG10()

```
LOG10(number);
```

Where ‘number’ is a numerical value whose base-10 logarithm is to be found out.

## Examples of MySQL LOG2()

Let us start by looking at a couple of basic examples. Let us find the values of log_{2} 10 and log_{2} 3. The query for it is:

```
SELECT LOG2(10);
SELECT LOG2(3);
```

And the output is –

### MySQL LOG2() With Negative Values

If we pass negative values to the `MySQL LOG2()`

function, it returns NULL. Let’s see this behavior using the below example.

```
SELECT LOG2(-4.2);
SELECT LOG2(-15);
```

And we get the output as,

### MySQL LOG2() With Zero

If we pass zero to the `LOG2()`

function, it returns NULL. Let us see this using the below example.

```
SELECT LOG2(0);
```

And we get the output as –

### LOG2() With Expressions

Let us write a query for the following expression using the `LOG2()`

function – 1 + 3 log_{2} 2.

```
SELECT 1+3*LOG2(2);
```

And we get the output as follows.

## Examples of MySQL LOG10()

Now let us look at a couple of basic examples of the `LOG10()`

function. Let us find the values of log_{10} 5 and log_{10} 10. The query for it is –

```
SELECT LOG10(5);
SELECT LOG10(10);
```

And the output is –

### MySQL LOG10() With Negative Values

If we pass negative values to the `LOG10()`

function, it returns NULL. Let’s see this behaviour using the below example.

```
SELECT LOG10(-4.2);
SELECT LOG10(-36);
```

And we get the output as,

### MySQL LOG10() With Zero

If we pass zero to the `LOG10()`

function, it returns NULL. Let us see this using the below example.

```
SELECT LOG10(0);
```

And we get the output as –

### LOG10() With Expressions

Let us write a query for the following expression using the `LOG10()`

function – 5 log_{10 }(5) + 3.

```
SELECT 5*LOG10(5)+3;
```

And we get the output as follows.

## Using LOG2() and LOG10() With Tables

Consider the below Numbers table.

### Simple Example

Using the `SELECT`

Statement, `LOG2()`

function and aliases, let us display the base-2 logarithm of the values in the X column. The query for it is –

```
SELECT ID, X, LOG2(X) AS LOG2_OF_X FROM Numbers;
```

And we get the output as follows –

Let us do something similar and find and display the base-10 logarithm of the values in the X column. Our query is –

```
SELECT ID, X, LOG10(X) AS LOG10_OF_X FROM Numbers;
```

And we get the output as,

### LOG2() and LOG10() with the UPDATE Statement

Let us now add two columns to the Numbers table which store the base-2 logarithm values and the base-10 logarithmic values of the X column.

Let us start by creating a column named `LOG2_OF_X`

of type float using the `ALTER`

statement. We will then add the base-2 logarithm values of the X column in it using the `UPDATE`

statement and finally display the new table. The query is –

```
ALTER TABLE Numbers ADD LOG2_OF_X float;
UPDATE Numbers SET LOG2_OF_X=LOG2(X);
SELECT * FROM Numbers;
```

And the output is,

Next, let us create a column named `LOG10_OF_X`

of type float using the `ALTER`

statement. We will then add the base-10 logarithm values of the X column in it using the `UPDATE`

statement and finally display the new table. The query is –

```
ALTER TABLE Numbers ADD LOG10_OF_X float;
UPDATE Numbers SET LOG10_OF_X=LOG10(X);
SELECT * FROM Numbers;
```

And we get the output as –

## Conclusion

Finding the logarithm of a number to the base-2 and base-10 is one of the most important and widely used logarithmic operations.