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17.1 Exponents and Logarithms

Mapping Function: exp (x)

Compute `e^x` for each element of x. To compute the matrix exponential, see Linear Algebra.

Mapping Function: expm1 (x)

Compute `exp (x) - 1` accurately in the neighborhood of zero.

Mapping Function: log (x)

Compute the natural logarithm, `ln (x)`, for each element of x. To compute the matrix logarithm, see Linear Algebra.

Function File: reallog (x)

Return the real-valued natural logarithm of each element of x. Report an error if any element results in a complex return value.

Mapping Function: log1p (x)

Compute `log (1 + x)` accurately in the neighborhood of zero.

Mapping Function: log10 (x)

Compute the base-10 logarithm of each element of x.

Mapping Function: log2 (x)
Mapping Function: [f, e] = log2 (x)

Compute the base-2 logarithm of each element of x.

If called with two output arguments, split x into binary mantissa and exponent so that `1/2 <= abs(f) < 1` and e is an integer. If `x = 0`, `f = e = 0`.

Mapping Function: pow2 (x)
Mapping Function: pow2 (f, e)

With one argument, computes 2 .^ x for each element of x.

With two arguments, returns f .* (2 .^ e).

Function File: nextpow2 (x)

If x is a scalar, return the first integer n such that 2^n ≥ abs (x).

If x is a vector, return `nextpow2 (length (x))`.

Function File: realpow (x, y)

Compute the real-valued, element-by-element power operator. This is equivalent to `x .^ y`, except that `realpow` reports an error if any return value is complex.

Mapping Function: sqrt (x)

Compute the square root of each element of x. If x is negative, a complex result is returned. To compute the matrix square root, see Linear Algebra.

Function File: realsqrt (x)

Return the real-valued square root of each element of x. Report an error if any element results in a complex return value.

Mapping Function: cbrt (x)

Compute the real cube root of each element of x. Unlike `x^(1/3)`, the result will be negative if x is negative.

Function File: nthroot (x, n)

Compute the n-th root of x, returning real results for real components of x. For example:

```nthroot (-1, 3)
⇒ -1
(-1) ^ (1 / 3)
⇒ 0.50000 - 0.86603i
```

x must have all real entries. n must be a scalar. If n is an even integer and X has negative entries, an error is produced.