Log vs Ln: Two Buttons, One Concept

Every scientific calculator has both. Picking the wrong one gives an answer that is off by a factor of 2.303.

If you have ever stared at a number on a form and wondered where it came from, you are not alone. Every scientific calculator has both. Picking the wrong one gives an answer that is off by a factor of 2.303.

log = log base 10

log(100) = 2 because 10² = 100. Used in engineering, decibels, pH.

ln = log base e (≈2.718)

ln(e²) = 2. Used in calculus, compound interest, physics, statistics.

Convert between them

log(x) = ln(x) / ln(10) ≈ ln(x) / 2.303.

Pro tips

  • Old textbooks sometimes use 'log' to mean ln — context is everything.
  • In computer science, 'log' often means base 2; check author convention.

Frequently asked questions

Why is ln 'natural'? It's the integral of 1/x dx, falls out of calculus naturally.

Can log be negative? Yes — log(0.1) = −1. log of zero or negative is undefined in real numbers.

Whatever number you land on, sanity-check it against a second method or a quick estimate in your head.

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