### 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.

> See also: log.

— Mapping Function: expm1 (x)

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

> See also: exp.

— Mapping Function: log (x)

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

> See also: exp, log1p, log2, log10, logspace.

— 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.

> See also: log, realpow, realsqrt.

— Mapping Function: log1p (x)

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

> See also: log, exp, expm1.

— Mapping Function: log10 (x)

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

> See also: log, log2, logspace, exp.

— 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`.

> See also: pow2, log, log10, exp.

— 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).

> See also: log2, nextpow2.

— 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`))`.

> See also: pow2, log2.

— 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.

> See also: reallog, realsqrt.

— 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.

> See also: realsqrt, nthroot.

— 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.

> See also: sqrt, realpow, reallog.

— 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.

> See also: nthroot.

— 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.

> See also: realsqrt, sqrt, cbrt.