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### 17.1 Exponents and Logarithms

exp (x)

  Compute `e^x` for each element of x.

  To compute the matrix exponential, see Linear Algebra.

  See also: log.

expm1 (x)

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

  See also: exp.

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.

reallog (x)

  Return the real-valued natural logarithm of each element of x.

  If any element results in a complex return value `reallog` aborts and issues an error.

  See also: log, realpow, realsqrt.

log1p (x)

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

  See also: log, exp, expm1.

log10 (x)

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

  See also: log, log2, logspace, exp.

log2 (x)
[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.

pow2 (x)
pow2 (f, e)

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

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

  See also: log2, nextpow2, power.

nextpow2 (x)

  Compute the exponent for the smallest power of two larger than the input.

  For each element in the input array x, return the first integer n such that 2^n ≥ abs (x).

  See also: pow2, log2.

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: power, reallog, realsqrt.

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.

realsqrt (x)

  Return the real-valued square root of each element of x.

  If any element results in a complex return value `realsqrt` aborts and issues an error.

  See also: sqrt, realpow, reallog.

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.

nthroot (x, n)

  Compute the real (non-complex) n-th root of x.

  x must have all real entries and n must be a scalar. If n is an even integer and x has negative entries then `nthroot` aborts and issues an error.

  Example:

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

  See also: realsqrt, sqrt, cbrt.

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