Raise a base to a power, or take the logarithm of a number to any base.
Calculated instantly in your browser.
How do you calculate exponents and logarithms?
An exponent raises a base to a power: result = base^exponent. A logarithm reverses it: log_base(x) = ln(x) ÷ ln(base), the power the base must be raised to in order to get x. They are inverses, so if b^x = y then log_b(y) = x. Example: 2^10 = 1024; log base 10 of 1000 = 3; log base 2 of 8 = 3.
Understanding your result
Exponents and logarithms are inverses: if bˣ = y then log_b(y) = x. Base 10 is the common log, base e the natural log (ln), base 2 common in computing.
Formula and method
Exponent: result = baseᵉˣᵖᵒⁿᵉⁿᵗ. Logarithm: log_base(x) = ln(x) ÷ ln(base), the power the base must be raised to in order to get x.
Assumptions and limitations
This tool evaluates powers and logarithms to any base you choose. Logarithms are undefined for zero and negative numbers, and the base must be positive and not equal to one, so those inputs return no result. Negative bases raised to fractional exponents are not real. Very large or very small results are limited by standard floating-point precision and may round.
Worked example
2¹⁰ = 1024; log base 10 of 1000 = 3; log base 2 of 8 = 3.
How to use this tool
- Choose exponent or logarithm.
- Enter the base (use e for natural).
- Enter the exponent or the number, and read the result.
Common mistakes to avoid
- Taking the logarithm of zero or a negative number.
- Using a base of 1 (a logarithm base must not be 1).
About the Exponent & Logarithm Calculator
The Exponent & Logarithm Calculator does both directions: raise a base to a power, or find the logarithm of a number to any base — including base 10, base 2 and natural log (base e).
Who should use this tool
Students and anyone needing quick powers, roots or logarithms without a scientific calculator.
Benefits
- Exponents and logarithms in one tool.
- Any base, including e for natural log.
- Shows a check so you can trust the result.
- Private and instant.
Practical use cases
- Computing 2¹⁰ or other powers.
- Finding log base 10 or natural log.
- Working with exponential growth and decay.
Frequently asked questions
What is a natural logarithm?
It is the logarithm to base e (about 2.718), written ln. Enter “e” as the base to compute it.
Can the exponent be negative or fractional?
Yes. A negative exponent gives a reciprocal, and a fractional exponent gives a root — for example a power of 0.5 is a square root.
Why won't it take the logarithm of a negative number?
Real logarithms are only defined for positive numbers, because no real power of a positive base produces a negative or zero result. Asking for the log of minus 4 or of zero therefore has no real answer. Logarithms of negative values exist only in complex mathematics, which this tool does not cover.