Quick answer

antilog_b(y) = b^y for b = 10, e, 2, or any valid n.

Formula

  • 10^y (common)
  • e^y (natural)
  • 2^y (binary)
  • n^y (custom)

Introduction

The base is not optional. It is encoded in the logarithm notation from the original problem, whether the book writes log, ln, or log with a subscript.

Two problems can share the same exponent y yet require different antilogs because the bases differ. That is why base selection is step one, not a shortcut you add at the end.

Compare bases side by side on the Antilog Calculator by changing only the base field while keeping y fixed.

Base comparison

Base 10: common logarithms in chemistry pH scales, decibels, Richter-style reporting, and introductory science courses that say "log" without a subscript.

Base e: natural logarithms in calculus, continuous compounding, population models, and statistics that label axes with ln.

Base 2: binary logarithms in computing and information theory; antilog_2(y) doubles the value each time y increases by 1 when you think in integer steps.

Custom n: any positive n ≠ 1 when the problem states log_n explicitly, such as base 5 growth drills in algebra.

All four cases still use the same symbolic rule collected in our antilog formula article, which lines up base 10, base e, and custom n in one view.

Formulas by base

Base 10: 10^y
Base e: e^y
Base 2: 2^y
Base n: n^y

Changing the base changes the answer even when y is identical. Treat the base as part of the question statement, not as a calculator default you override casually.

After you choose b, run the arithmetic with the same substitution habit used in antilog examples so you practice reading notation and evaluating b^y in one motion.

Choosing a base

  1. Read the log notation. Plain log often means base 10 in science classes. ln means base e. log_2 or log_5 states the base in the symbol.
  2. Select the matching power. Do not substitute 10 when the problem used ln. Do not use e^y when the sheet said common log.
  3. Estimate before you calculate. For base 10, integer y gives powers of ten you can predict. For base e, remember e^1 ≈ 2.7 and e^2 ≈ 7.4 as sanity checks.
  4. Compare if the wording is unclear. Compute two candidates only when the problem is ambiguous. Usually the chapter topic tells you which base the course expects.

Same y, different bases

Let y = 3. Base 10 gives 1000. Base 2 gives 8. Base e gives about 20.09. Same exponent, three different antilogs.

Let y = 1. Base 10 gives 10. Base e gives about 2.718. The gap is large even for a small exponent.

This contrast is why teachers mark base selection before they mark the final number.