Quick answer

Compute b^y where y is the logarithm value and b is the original log base.

Formula

  • Step 1: read y
  • Step 2: read b
  • Step 3: compute b^y
  • Step 4: verify log_b(result) = y

Introduction

Calculating an antilog is exponentiation with the correct base. The process is short on paper, but skipping a step is what creates the usual base-switch errors in student work.

Teachers reward clear setup: write the log equation, circle the base, then show the power before you touch calculator buttons.

Use the Antilog Calculator at the end of each problem to verify manual work without skipping your written steps.

Before you start

Confirm whether the problem used log_10, ln, or log_b. That single decision fixes the base for your antilog.

Copy the full equation log_b(x) = y onto your paper. Circle y and b in different colors if that helps you slow down.

Open the antilog formula reference if you need the base 10 and natural forms written next to each other before you calculate.

Calculation rule

antilog_b(y) = b^y
Check: log_b(b^y) = y

Scientific calculators provide 10^x and e^x keys for the most common cases. Custom bases use the power key, the caret, or a spreadsheet function such as POWER(b, y).

After you master the routine, strengthen speed with varied numbers in antilog examples, which walks through base 10, natural, and fractional exponent cases.

Step-by-step method

  1. Identify the logarithmic value. Extract y from the equation, graph label, or table. If the problem gives log_10(x) = 2.5, then y is 2.5.
  2. Determine the base. Use 10 for common log, e for natural log, or the stated base b in log_b notation.
  3. Apply exponentiation. Evaluate b^y with exponent laws for simple integers, otherwise use a calculator. Write the power line before you press equals.
  4. Verify the result. Compute log_b of your answer on the same calculator mode. You should return to the original y within rounding tolerance.
  5. Record units and rounding. Science problems need units on the final antilog answer. Round only at the end unless your rubric says otherwise.

Full walkthrough

Problem: log_2(x) = 6. Here y = 6 and b = 2. Antilog form: x = 2^6 = 64.

Check: log_2(64) = 6 because 2^6 equals 64.

Problem: log_10(x) = 1.477. Then x = 10^1.477 ≈ 30.0 after calculator evaluation and careful rounding.