Logarithm of Infinity

What is the logarithm of infinity?

log₁₀(∞) = ?

 

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 log₁₀(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 log₁₀(x) is undefined

  x → -∞

 

Logarithm of negative number ►

 

---

See also

• Logarithm of zero
• Logarithm of one
• Logarithm of negative number
• Logarithm calculator
• Natural logarithm calculator
• Natural logarithm
• e constant
• Decibel (dB)