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# log10

Common logarithm (base 10)

## 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