Natural Logarithm of Infinity


Natural Logarithm of Infinity

What is the natural logarithm of infinity?

ln(∞) = ?

Since infinity is not a number, we should use limits:


x approaches infinity

The limit of the natural logarithm of x when x approaches infinity is infinity:

lim ln(x) = ∞



x approaches minus infinity

The opposite case, the natural logarithm of minus infinity is undefined for real numbers, since the natural logarithm function is undefined for negative numbers:

lim ln(x) is undefined

  x → -∞


So we can summarize

ln(∞) = ∞


ln(-∞) is undefined


Ln of negative number


See also

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