Antilog Calculator

Calculate antilogarithms (inverse logarithms) with any base including base 10 and natural antilog

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Expression:

log() Antilog Comparison

Step-by-Step Solution

Real-World Applications

Antilog Reference Table

x 10ˣ

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About Antilog Calculator

What is an Antilogarithm?

An antilogarithm (antilog) is the inverse operation of a logarithm. If log_b(x) = y, then the antilogarithm of y with base b equals x. In other words, antilog_b(y) = b^y = x.

How to Use This Calculator

  1. Enter the exponent value (x): This is the power to which the base will be raised
  2. Select or enter the base (b): Common options include 10, 2, or e (Euler's number)
  3. View instant results: See the antilog value with step-by-step explanation
  4. Explore common values: Use the quick examples and reference tables

Antilog Formula

The antilogarithm formula is:

antilog_b(x) = b^x

Where:

  • b = base of the logarithm
  • x = the logarithmic value (exponent)
  • Result = the original number

Common Antilogarithm Types

Type Base Formula Example
Common Antilog 10 10^x antilog₁₀(2) = 10² = 100
Natural Antilog e ≈ 2.718 e^x antilogₑ(1) = e¹ ≈ 2.718
Binary Antilog 2 2^x antilog₂(3) = 2³ = 8

Applications of Antilogarithms

Science & Engineering

  • Converting logarithmic scales back to linear values
  • Calculating pH to hydrogen ion concentration: [H⁺] = 10^(-pH)
  • Converting decibels to power ratios
  • Exponential growth and decay calculations

Finance

  • Compound interest final values
  • Growth rate calculations
  • Present/future value conversions

Computer Science

  • Inverse log transformations in algorithms
  • Machine learning probability calculations
  • Data normalization reversals

Common Antilog Values Reference

x 10^x e^x 2^x
0 1 1 1
1 10 2.718 2
2 100 7.389 4
3 1,000 20.09 8
4 10,000 54.60 16
5 100,000 148.4 32

Note: The antilogarithm is always positive for real number bases (b > 0, b ≠ 1). Negative exponents produce fractional results (e.g., 10^(-2) = 0.01).

Key Concepts

  • Antilog and Log Relationship: If log₍ᵦ₎(x) = y, then antilog₍ᵦ₎(y) = x
  • Base 10 (Common): 10ˣ is the inverse of log₁₀(x)
  • Base e (Natural): eˣ is the inverse of ln(x)
  • Negative Exponents: b⁻ˣ = 1/bˣ produces fractions
  • Zero Exponent: b⁰ = 1 for any valid base b