numpy.log(x[, out]) = <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.


x : array_like

Input value.


y : ndarray

The natural logarithm of x, element-wise.

See also

log10, log2, log1p, emath.log


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.


[R44]M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”, 10th printing, 1964, pp. 67.
[R45]Wikipedia, “Logarithm”.


>>> np.log([1, np.e, np.e**2, 0])
array([  0.,   1.,   2., -Inf])

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