Antilog Calculator – Antilogarithm
Calculate antilogarithm (inverse logarithm) for any base with step-by-step solutions
Calculate Antilogarithm
Quick Examples
The logarithm value to find the antilog of
Most common logarithm base
Antilogarithm Result
Step-by-Step Calculation:
1. Given: log_10(x) = 0
2. To find antilog, we calculate: x = 10^0
3. x = 10^0
4. x = 1
Verification:
Original logarithm: 0
log_10(1) = 0.00000000
Difference: 0.00e+0 (should be ≈ 0)
✅ Calculation verified!
Additional Information
In other bases:
Base e: e^0.0000 = 1
Base 2: 2^0.0000 = 1
Properties:
Result = 1 (log = 0)
Magnitude: 0.00 orders of magnitude
Example: Finding Antilog₁₀(3)
Problem
Find the antilog of 3 with base 10
This means: if log₁₀(x) = 3, what is x?
Solution
Given: log₁₀(x) = 3
Formula: x = 10³
Calculation: x = 10 × 10 × 10
Result: x = 1000
Verification: log₁₀(1000) = 3 ✓
Key Formulas
Antilogarithm
x = b^y
Where y is the logarithm and b is the base
Logarithm (inverse)
y = log_b(x)
The logarithm is the inverse of antilog
Relationship
log_b(b^y) = y
Logarithm and antilog cancel out
Common Logarithm Bases
Common Logarithm
Used in pH, decibels, Richter scale
Natural Logarithm
Growth, decay, calculus (e ≈ 2.71828)
Binary Logarithm
Computer science, information theory
Quick Reference
Understanding Antilogarithms
What is an Antilogarithm?
An antilogarithm (or antilog) is the inverse function of a logarithm. If the logarithm of a number x to base b is y, then the antilogarithm of y to base b is x. In mathematical terms: if log_b(x) = y, then antilog_b(y) = x.
The Relationship
- •Logarithm asks: "To what power must we raise the base to get this number?"
- •Antilogarithm answers: "What number do we get when we raise the base to this power?"
- •They are inverse operations that "undo" each other
Applications
Science & Engineering
pH calculations, decibel conversions, Richter scale
Finance
Compound interest, exponential growth calculations
Computer Science
Algorithm complexity, binary operations
Statistics
Log-normal distributions, data transformation
Important Properties
Identity: antilog_b(log_b(x)) = x
Zero power: antilog_b(0) = 1
Unit log: antilog_b(1) = b
Negative logs: antilog_b(-y) = 1/antilog_b(y)
Addition rule: antilog_b(x + y) = antilog_b(x) × antilog_b(y)
Multiplication rule: antilog_b(n × y) = [antilog_b(y)]^n