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.
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.