# log10

Common logarithm (base 10)

## Syntax

``Y = log10(X)``

## Description

example

````Y = log10(X)` returns the common logarithm of each element in array `X`. The function accepts both real and complex inputs. For real values of `X` in the interval (0, `Inf`), `log10` returns real values in the interval (`-Inf` ,`Inf`). For complex and negative real values of `X`, the `log10` function returns complex values.```

## Examples

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Examine several values of the base 10 logarithm function.

Calculate the common logarithm of 1.

`log10(1)`
```ans = 0 ```

The result is `0`, so this is the x-intercept of the `log10` function.

Calculate the common logarithm of 10.

`log10(10)`
```ans = 1 ```

The result is `1` since $1{0}^{1}=10$.

Calculate the common logarithm of 100.

`log10(100)`
```ans = 2 ```

The result is `2` since $1{0}^{2}=100$.

Calculate the common logarithm of 0.

`log10(0)`
```ans = -Inf ```

The result is `-Inf` since $1{0}^{-\infty }=0$.

Create a vector of numbers in the interval `[0.5 5]`.

`X = (0.5:0.5:5)';`

Calculate the common logarithm of `X`.

`Y = log10(X)`
```Y = 10×1 -0.3010 0 0.1761 0.3010 0.3979 0.4771 0.5441 0.6021 0.6532 0.6990 ```

Create two Cartesian grids for `X` and `Y`.

`[X,Y] = meshgrid(0:0.5:1.5,-2:0.5:2);`

Calculate the complex base 10 logarithm $lo{g}_{10}\left(X+iY\right)$ on the grid. Use `1i` for improved speed and robustness with complex arithmetic.

`Z = log10(X + 1i*Y)`
```Z = 9×4 complex 0.3010 - 0.6822i 0.3142 - 0.5758i 0.3495 - 0.4808i 0.3979 - 0.4027i 0.1761 - 0.6822i 0.1990 - 0.5425i 0.2559 - 0.4268i 0.3266 - 0.3411i 0.0000 - 0.6822i 0.0485 - 0.4808i 0.1505 - 0.3411i 0.2559 - 0.2554i -0.3010 - 0.6822i -0.1505 - 0.3411i 0.0485 - 0.2014i 0.1990 - 0.1397i -Inf + 0.0000i -0.3010 + 0.0000i 0.0000 + 0.0000i 0.1761 + 0.0000i -0.3010 + 0.6822i -0.1505 + 0.3411i 0.0485 + 0.2014i 0.1990 + 0.1397i 0.0000 + 0.6822i 0.0485 + 0.4808i 0.1505 + 0.3411i 0.2559 + 0.2554i 0.1761 + 0.6822i 0.1990 + 0.5425i 0.2559 + 0.4268i 0.3266 + 0.3411i 0.3010 + 0.6822i 0.3142 + 0.5758i 0.3495 + 0.4808i 0.3979 + 0.4027i ```

## Input Arguments

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Input array, specified as a scalar, vector, matrix, or multidimensional array.

Data Types: `single` | `double`
Complex Number Support: Yes

## Version History

Introduced before R2006a