# Logarithm of Infinity

What is the logarithm of infinity?

log_{10}(∞) = ?

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

### x approaches infinity

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

lim log_{10}(*x*) = ∞

*x*→∞

### x approaches minus infinity

The opposite case, the logarithm of minus infinity (-∞) is undefined for real numbers, since the logarithmic function is undefined for negative numbers:

lim log_{10}(*x*) is undefined

*x *→ -∞

Logarithm of negative number ►