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# log

Logarithm in Galois field

## Syntax

```y = log(x) ```

## Description

`y = log(x) ` computes the logarithm of each element in the Galois array `x`. `y` is an integer array that solves the equation `A.^y = x`, where `A` is the primitive element used to represent elements in `x`. More explicitly, the base `A` of the logarithm is `gf(2,x.m)` or `gf(2,x.m,x.prim_poly)`. All elements in `x` must be nonzero because the logarithm of zero is undefined.

## Examples

The code below illustrates how the logarithm operation inverts exponentiation.

```m = 4; x = gf([8 1 6; 3 5 7; 4 9 2],m); y = log(x); primel = gf(2,m); % Primitive element in the field z = primel .^ y; % This is now the same as x. ck = isequal(x,z)```

The output is

```ck = 1 ```

The code below shows that the logarithm of `1` is `0` and that the logarithm of the base (`primel`) is `1`.

```m = 4; primel = gf(2,m); yy = log([1, primel])```

The output is

```yy = 0 1```

## See Also

Introduced before R2006a

## Support

#### Bridging Wireless Communications Design and Testing with MATLAB

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