Quick answer

Every example follows antilog_b(y) = b^y.

Formula

  • 10^3 = 1000
  • e^2 ≈ 7.389
  • 2^5 = 32
  • 10^(-2) = 0.01

Introduction

Examples turn the formula into muscle memory faster than definitions alone. Copy the setup line every time, even when the numbers look easy.

Mix base 10, natural, and custom bases in one study session so you practice base selection as well as arithmetic.

The Antilog Calculator helps you check final values after you show manual work on homework.

Types of examples

Base 10 problems dominate introductory algebra and science labs that use common logarithms or decibel-style reasoning.

Natural antilog problems appear in calculus, continuous growth models, and statistics courses that use ln on graphs.

Custom bases such as 2 or 5 test whether you truly apply b^y instead of guessing from calculator habits built only on base 10.

Review the procedural checklist in how to calculate an antilog if you want a four-step template to accompany each example below.

Pattern to copy

Write log_b(x) = y
Rewrite x = b^y
Evaluate the power
Verify log_b(x) = y

Stating the base in words prevents silent mistakes. Write "base 10 antilog" or "natural antilog" in the margin before you enter numbers.

When you compare how different bases change the output for the same y, use common antilog bases as a companion reference table.

Worked problems

  1. Base 10 drill. y = 4 means 10^4 = 10,000. Negative y such as -2 gives 10^(-2) = 0.01.
  2. Natural antilog drill. y = 0.5 with base e gives e^0.5 = √e ≈ 1.649. y = 2 gives e^2 ≈ 7.389.
  3. Custom base drill. y = 2 with base 5 gives 5^2 = 25. The base digit is part of the instructions, not a guess.
  4. Verification habit. After each result, take log_b on your calculator to confirm you return to the starting y.

Educational exercises

Given log_10(x) = 1.3010 (approximate), antilog ≈ 10^1.3010 ≈ 20. This mirrors classic log-table practice where students read mantissas and characteristics.

Given log_2(x) = 10, antilog = 2^10 = 1024, a common computer science checkpoint.

Always state the base when you hand in work. Teachers check base selection before they mark arithmetic.