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→∞

 

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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