Quick answer

General: antilog_b(y) = b^y. Base 10: Antilog(x) = 10^x. Natural: e^y = exp(y).

Formula

  • antilog_b(y) = b^y
  • Antilog(x) = 10^x
  • exp(y) = e^y

Introduction

Every antilog calculation is a power. The only real decision is which base belongs in that power.

Reference sheets often list separate lines for common and natural antilogs even though the structure is identical. Learning one general pattern prevents memorizing unrelated rules.

After you choose the correct form, use the Antilog Calculator to confirm numeric results and study the live formula line.

Formula explanation

Base 10 antilog is written Antilog(x) = 10^x on many formula cards. In that line, the symbol x stands for the logarithm value from a common log, not the final unknown from your word problem. Read the legend on your sheet if symbols shift meaning.

Natural antilog replaces 10 with e. Calculators label the key exp, e^x, or inverse ln depending on the brand. All of them compute e raised to the displayed exponent.

For any other approved base n, antilog_n(y) = n^y. Custom bases appear in computer science, information theory, and specialized engineering formulas where log_2 or log_5 is stated explicitly.

If you need the vocabulary behind the symbols, revisit what is an antilog for a plain-language definition before you memorize more notation.

All forms on one line

antilog_b(y) = b^y
10^y for common antilog
e^y for natural antilog
n^y for base n stated in the problem

Mathematical interpretation: the antilog restores the argument of the logarithm by applying the exponent y to the base. You are not "undoing" addition or multiplication. You are applying a power.

Choosing the base is easier when you compare typical courses side by side in common antilog bases, which shows how the same exponent y produces different answers for 10, e, and 2.

Using each formula

  1. Match the log base to a power form. Common log notation implies 10^y. Natural log notation implies e^y. Stated log_n implies n^y.
  2. Substitute the logarithm value. Place the given y in the exponent position exactly. Do not multiply the base by y.
  3. Evaluate with calculator or laws. Integer exponents can be expanded by hand. Decimals usually require a calculator or spreadsheet power function.
  4. Label the answer with context. Write units and round only at the end if your science teacher requires significant figures.

Base 10 vs base e

log_10(1000) = 3 gives antilog_10(3) = 10^3 = 1000. The exponent 3 was visible in the log statement the entire time.

ln(7.389) ≈ 2 gives e^2 ≈ 7.389. Same structure, different base. A base switch would have produced a different number even with the same y.

log_2(32) = 5 gives 2^5 = 32, a reminder that custom bases follow the identical power pattern.