Antilog Calculator
Calculate antilogarithms (inverse logarithms) with any base including base 10 and natural antilog
Expression:
log() 10, e, 2 =
log() Antilog Comparison
10
Common Antilog
e
Natural Antilog
2
Binary Antilog
10
Common Antilog
e
Natural Antilog
2
Binary Antilog
Step-by-Step Solution
Real-World Applications
Antilog Reference Table
| x | 10ˣ | eˣ | 2ˣ |
|---|---|---|---|
If you like this calculator
Please help us simply by sharing it. It will help us a lot!
Related Calculators
Other calculators you might find useful.
Triangle Calculator
Calculate sides, angles, area, and perimeter of any triangle using 6 different solving methods
Cone Calculator
Calculate volume, surface area, slant height, and other properties of a cone
Inverse Variation Calculator
Calculate inverse variation relationships where xy = k (constant)
Derivative Calculator
Calculate derivatives and find the slope of functions at any point
Area Calculator
Calculate the area of rectangles, circles, triangles, and other 2D shapes instantly
Fraction to Percent Calculator
Convert fractions to percentages instantly with step-by-step solutions
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
- Enter the exponent value (x): This is the power to which the base will be raised
- Select or enter the base (b): Common options include 10, 2, or e (Euler's number)
- View instant results: See the antilog value with step-by-step explanation
- 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