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Natural logarithm


Y = log(X)



Y = log(X) returns the natural logarithm ln(x) of each element in array X.

The log function’s domain includes negative and complex numbers, which can lead to unexpected results if used unintentionally. For negative and complex numbers z = u + i*w, the complex logarithm log(z) returns

log(abs(z)) + 1i*angle(z)

If you want negative and complex numbers to return error messages rather than return complex results, use reallog instead.


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Show that the natural logarithm of -1 is iπ.

ans = 0.0000 + 3.1416i

Input Arguments

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Input array, specified as a scalar, vector, matrix, or multidimensional array.

Data Types: single | double
Complex Number Support: Yes

Output Arguments

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Logarithm values, returned as a scalar, vector, matrix, or multidimensional array.

For positive real values of X in the interval (0, Inf), Y is in the interval (-Inf,Inf). For complex and negative real values of X, Y is complex. The data type of Y is the same as that of X.

Extended Capabilities

Introduced before R2006a