Logarithm of Negative Number

What is the logarithm of a negative number?

The logarithmic function

y = log_b(x)

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(x) is undefined for x ≤ 0

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

log₁₀(-5) is undefined

 

 

Logarithm of zero ►

 

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See also

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