Algebra
Solve for Exponents
b^n
=
r
Base (b)
Exponent (n)
Result (r)
Solve for Exponents Calculator
Whether you know the base and exponent and need the result, or need to work backward to find a missing exponent or base, this calculator solves all three directions of the exponent equation.
How to use this calculator
- Choose what to solve for: Result, Exponent, or Base.
- Enter the other two known values (Base, Exponent, and/or Result).
- Read the calculated missing value.
What this calculator does
Given the equation b^n = r (base raised to an exponent equals a result), this calculator solves for whichever one of the three variables you don’t already know, using the appropriate inverse operation for each case.
Solve for Result: r = b^n
Solve for Exponent: n = log(r) / log(b)
Solve for Base: b = r^(1/n)
Solve for Exponent: n = log(r) / log(b)
Solve for Base: b = r^(1/n)
Why solving for the exponent needs logarithms
Finding the result from a known base and exponent is straightforward exponentiation, but working backward to find the exponent itself requires a logarithm, since the exponent is “buried” inside the exponentiation operation and logarithms are specifically the inverse operation that extracts it. This is a common sticking point in algebra, this calculator handles the logarithm calculation automatically.
Frequently asked questions
How do I find the exponent if I know the base and result?
Use a logarithm: n = log(r) / log(b), where r is the result and b is the base, this is the inverse operation needed to extract an exponent that’s otherwise “hidden” inside the exponentiation.
How do I find the base if I know the exponent and result?
Take the result to the power of 1 divided by the exponent: b = r^(1/n), this is equivalent to taking the nth root of the result.