# log10

Common logarithm (base 10)

## Syntax

• ``Y = log10(X)``
example

## 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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### Calculate Scalar Common Logarithm Values

Examine several values of the base 10 logarithm function.

Calculate the common logarithm of 1.

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

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

Calculate the common logarithm of 10.

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

The result is `1` since `10^1 = 10`.

Calculate the common logarithm of 100.

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

The result is `2` since `10^2 = 100`.

Calculate the common logarithm of 0.

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

The result is `-Inf` since ```10^(-Inf) = 0```.

### Real-Valued Common Logarithm

Create a vector of real numbers in the interval `[0.5,10]`.

```X = (0.5:0.5:10)'; ```

Calculate the common logarithm of `X`.

```Y = log10(X) ```
```Y = -0.3010 0 0.1761 0.3010 0.3979 0.4771 0.5441 0.6021 0.6532 0.6990 0.7404 0.7782 0.8129 0.8451 0.8751 0.9031 0.9294 0.9542 0.9777 1.0000 ```

### Complex-Valued Common Logarithm

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 on the grid. Use `1i` for improved speed and robustness with complex arithmetic.

```Z = log10(X + 1i*Y) ```
```Z = 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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### `X` — Input arrayscalar | vector | matrix | multidimensional array

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

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