Work out natural logarithm instantly with clear inputs, formula shown and shareable results.
The natural logarithm answers the question 'e to what power gives x?'. It is the inverse of the exponential function, so ln(eˣ) = x, and its derivative 1/x makes it the backbone of calculus with growth and decay.
Natural logarithm
ln x = y ⇔ eʸ = x
Conversion
log₁₀ x = ln x / ln 10
About 2.9957323, since e² ≈ 7.389 and e³ ≈ 20.086.
No real power of e produces zero or a negative number, so the function has no real value there.