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# numpy.log

numpy.log(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature]) = <ufunc 'log'>

  Natural logarithm, element-wise.

  The natural logarithm `log` is the inverse of the exponential function, so that log(exp(x)) = x. The natural logarithm is logarithm in base `e`.

  Parameters:
    x array_like

      Input value.

    out ndarray, None, or tuple of ndarray and None, optional

      A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs.

    where array_like, optional

      This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default `out=None`, locations within it where the condition is False will remain uninitialized.

    **kwargs

      For other keyword-only arguments, see the ufunc docs.

  Returns:
    y ndarray

      The natural logarithm of x, element-wise. This is a scalar if x is a scalar.

  See also

  `log10`, `log2`, `log1p`, `emath.log`

  Notes

  Logarithm is a multivalued function: for each x there is an infinite number of z such that exp(z) = x. The convention is to return the z whose imaginary part lies in (-pi, pi].

  For real-valued input data types, `log` always returns real output. For each value that cannot be expressed as a real number or infinity, it yields `nan` and sets the invalid floating point error flag.

  For complex-valued input, `log` is a complex analytical function that has a branch cut [-inf, 0] and is continuous from above on it. `log` handles the floating-point negative zero as an infinitesimal negative number, conforming to the C99 standard.

  In the cases where the input has a negative real part and a very small negative complex part (approaching 0), the result is so close to -pi that it evaluates to exactly -pi.

  References

  [1]

  M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”, 10th printing, 1964, pp. 67. https://personal.math.ubc.ca/~cbm/aands/page_67.htm

  [2]

  Wikipedia, “Logarithm”. https://en.wikipedia.org/wiki/Logarithm

  Examples

      >>> import numpy as np
      >>> np.log([1, np.e, np.e**2, 0])
      array([  0.,   1.,   2., -inf])