The exponential function eˣ is the unique function equal to its own derivative. It describes continuous compound growth, radioactive decay, population models, the normal distribution and the charging of capacitors.
How to use the e Power x Calculator
- Exponent x
- Every result field is editable: type into eˣ and Exponent x plus every other field update to match.
Results update as you type, and everything is calculated in your browser.
How it works
Enter x, or type into the eˣ field to find x = ln(value).
What each result means
- eˣ = exp([Exponent x])
- e⁻ˣ = exp(-[Exponent x])
- log₁₀(eˣ) = [Exponent x]÷ln(10)
Example values
How the main result changes when Exponent x changes and everything else stays at the example values above:
| Exponent x | eˣ |
|---|---|
| 1 | 2.7183 |
| 1.5 | 4.4817 |
| 2 | 7.3891 |
| 2.5 | 12.1825 |
| 3 | 20.0855 |
| 4 | 54.5982 |
Formula
eˣ = Σ xᵏ/k!, e ≈ 2.718281828459045
Worked example
Inputs — Exponent x: 2.
Results — eˣ = 7.389056098931; e⁻ˣ = 0.135335283237; log₁₀(eˣ) = 0.868588963807.
Key terms
- Exponential function
- f(x) = eˣ.
Frequently asked questions
What is e?
Euler's number, ≈ 2.71828, the base of natural growth.
What is e⁰?
1.
Is eˣ ever negative?
No – it is positive for every real x.
How is eˣ related to compound interest?
(1 + r/n)ⁿᵗ → eʳᵗ as compounding becomes continuous.