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