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Exponent & Logarithm Calculator

The defaults compute 2^10 = 1,024. This calculator puts three related operations in one place — raise x to the power y, take the logarithm of y in base x, or take the nth root of x; logarithms of any base use the change-of-base identity ln(y) / ln(x), and roots are computed as fractional powers, since the nth root of x equals x^(1/n).

Result
1,024
Inputs
Operation
^
Any nonzero base to the 0 power is 1
x^0 = 1 for every nonzero x, and x^1 = x. A negative exponent gives a reciprocal: x^(−n) = 1/xⁿ.
Powers, logs, and roots invert each other
If x^y = z, then logₓ(z) = y and ʸ√z = x — the three operations are just different views of one relationship.
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Uses your inputs above
1,024 result. Want to try a variation?

The math

Reviewed 2026
Formula
logₐ(b) = ln(b)/ln(a); ⁿ√x = x^(1/n)

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Example: how exponent / log is calculated

Step-by-step with default inputs

Suppose you put the default values into Exponent & Logarithm Calculator:

Operation
x^y
x
2
y
10

Plug those into the formula logₐ(b) = ln(b)/ln(a); ⁿ√x = x^(1/n) and the result is:

Result
1,024

How does the exponent & logarithm calculator work?

Exponent & Logarithm Calculator uses the formula shown in the math card and is computed from first principles. Inputs are validated for sensible ranges; results are computed client-side for instant feedback and do not leave your browser.

Last reviewed July 2, 2026 · Editorial policy

Frequently asked questions

How do you calculate a logarithm with any base?

Divide natural logs: log base x of y equals ln(y) ÷ ln(x). For example, log base 2 of 10 is ln(10) ÷ ln(2) ≈ 3.3219 — which checks out, since 2^3.3219 ≈ 10. This change-of-base identity is exactly what the calculator's log mode computes.

How are roots and exponents related?

A root is a fractional exponent: the nth root of x is x^(1/n), so the square root of 2 is 2^0.5 and the 10th root of 2 is 2^0.1 ≈ 1.0718. That is why one calculator covers both — the root mode just computes a power.

What is 2 to the power of 10?

1,024 — start at 2 and double nine more times: 2, 4, 8, 16, 32, 64, 128, 256, 512, 1,024. Each unit added to the exponent multiplies the result by the base again, and any positive base to the power 0 is 1.

How accurate is this exponent / log calculator?

The math is deterministic — the same inputs always produce the same output, and the formula is shown above. Accuracy of the answer for your situation depends on how well your inputs match reality and how well the formula models the question.

How do I share my result?

Hit Share at the top of the page. Every input you change is encoded in the URL, so a permalink reproduces exactly what you see. No account needed.