What is the logarithm of a negative number?

The logarithmic function

*y* = log* _{b}*(

is the inverse function of the exponential function

*x* =* b ^{y}*

Since the base b is positive (b>0), the base b raised to the
power of y must be positive (b^{y}>0) for any real y. So the
number x must be positive (x>0).

The real base b logarithm of a negative number is undefined.

log* _{b}*(

For example, the base 10 logarithm of -5 is undefined:

log_{10}(-5) is undefined

For complex number z in polar form:

*z* = r·*e*^{iθ}

The complex logarithm:

Log z = ln r + iθ

Is defined for negative z.

- Logarithm of zero
- Logarithm of one
- Logarithm of infinity
- Logarithm calculator
- Natural logarithm calculator
- Natural logarithm
- e constant

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