Formulas
- Power: aᵇ = a multiplied by itself b times
- Root: the b-th root of a = a^(1/b)
- Logarithm: log_b(a) = ln(a) ÷ ln(b), the exponent you must raise b to in order to get a
Example
With a = 8 and b = 2: 8² = 64, √8 = 2.828427 and log₂ 8 = 3, because 2³ = 8.
Rules worth knowing
- a⁰ = 1 and a⁻ᵇ = 1 ÷ aᵇ.
- log(x × y) = log x + log y.
- Even roots of negative numbers are not real numbers; odd roots are (∛−8 = −2).
Frequently asked questions
What is ln?
The natural logarithm, in base e ≈ 2.718. It appears in compound interest, growth and decay.
Why is the log of a negative number “not defined”?
No real power of a positive base gives a negative number, so the logarithm only exists for positive values.
See also
Results are estimates for information only and are not financial, legal or medical advice. Rates, taxes and fees vary — confirm with a professional or your lender.