Mathematics · Algebra
Exponent, Root & Logarithm Calculator
Raise a number to any power (including negative and fractional exponents), take square, cube or any n-th root (real roots of negative numbers too), find logarithms in base 10, e, 2 or any base, and solve exponential equations aˣ = y.
Your inputs
Quick start — try a typical case
Your result Live
2¹⁰
1,024
2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
- Scientific Notation
- 1.024 × 10³
- Number of Digits
- 4
How this is calculated
aᵇ · ⁿ√x = x^(1/n) · log_b(x) = ln x ÷ ln b · aˣ = y ⇒ x = log y ÷ log a
- e
- Euler's number, 2.718281828…
An exponent says how many times to multiply a number by itself; a negative exponent means one over that, and a fractional exponent is a root. A logarithm undoes a power: log₁₀ 1000 = 3 because 10³ = 1000. Any log can be found from natural logs with the change-of-base rule, which also solves equations like 2ˣ = 1024.
Assumptions & sources
- Real numbers only; complex results (like √−1) aren't shown.
Calculator ID MATH-POWERS-001 · version 1.0.0
Common questions
What is 2 to the power 10?
1,024.
How do I find a cube root?
Raise to the power 1/3: ∛1000 = 10 because 10 × 10 × 10 = 1000.
What's the difference between log and ln?
log usually means base 10; ln is the natural log, base e ≈ 2.718. ln x = log x × 2.302585…