The rule
antilogₐ(y) = aʸ
Why it works
The antilogarithm is just exponentiation seen from the other side. Where a logarithm asks 'to what power?', the antilogarithm answers 'this power gives what?'. They undo each other exactly.
How to do it by hand
- Take the base
- Raise it to the value of the logarithm
- That result is the antilogarithm
- Check by taking the log of the answer: you get your value back
What is worth knowing
The word survives from the era of log tables, where finding an antilog meant reading the table backwards — a genuinely separate operation. On a modern calculator it is just the power key, which is why the term is fading. It still turns up where logarithmic scales are converted back: going from decibels to a power ratio, or from pH to a hydrogen ion concentration, is an antilog. A pH of 3 means a concentration of 10⁻³ molar, and moving one pH unit is a tenfold change, which is exactly why the scale is logarithmic.