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

 

 

Natural logarithm of negative number ►

 

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See also

• Ln of zero
• Ln of one
• Ln of e
• Ln of negative number
• Logarithm calculator
• Natural logarithm calculator
• Natural logarithm
• e constant