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Compute the natural logarithm of `x`.
Return the "principal value" (for a description of this, see `numpy.log`)
of :math:`log_e(x)`. For real `x > 0`, this is a real number (``log(0)``
returns ``-inf`` and ``log(np.inf)`` returns ``inf``). Otherwise, the
complex principle value is returned.
Parameters
----------
x : array_like
The value(s) whose log is (are) required.
Returns
-------
out : ndarray or scalar
The log of the `x` value(s). If `x` was a scalar, so is `out`,
otherwise an array is returned.
See Also
--------
numpy.log
Notes
-----
For a log() that returns ``NAN`` when real `x < 0`, use `numpy.log`
(note, however, that otherwise `numpy.log` and this `log` are identical,
i.e., both return ``-inf`` for `x = 0`, ``inf`` for `x = inf`, and,
notably, the complex principle value if ``x.imag != 0``).
Examples
--------
>>> np.emath.log(np.exp(1))
1.0
Negative arguments are handled "correctly" (recall that
``exp(log(x)) == x`` does *not* hold for real ``x < 0``):
>>> np.emath.log(-np.exp(1)) == (1 + np.pi * 1j)
True
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