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 |
|---|---|---|---|
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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
- 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