Exponentiation, Logarithm, Nth Root FAQ
What does this exponentiation, logarithm, and nth root calculator do?
This calculator solves three equivalent forms of the same relationship: a = \sqrt[x]{b}, b = a^x, and x = log_a b. You can use it as an exponent calculator, logarithm calculator, or nth root calculator.
Which variable should I choose to solve exponentiation, logarithm, or nth root?
Choose B to solve the exponentiation form b = a^x. Choose X to solve the logarithm form x = log_a b. Choose A to solve the root form a = \sqrt[x]{b}.
What is the formula linking powers, logs, and roots?
The equivalent forms are b = a^x, x = log_a b, and a = \sqrt[x]{b}. If you know any two of the three values, the third can be calculated from the same relationship.
How do you calculate a logarithm with any base?
A logarithm can be calculated with the change-of-base formula log_a b = log(b) / log(a). This calculator applies that relationship directly when solving for x.
How do you calculate the natural logarithm?
The natural logarithm is the logarithm with base e, so ln(b) = log_e b. In this calculator, enter A = e ≈ 2.71828, enter your value as B, and choose X to calculate ln(b).
How do you calculate an nth root?
An nth root can be written as a power: \sqrt[x]{b} = b^(1/x). For example, the cube root of 8 is 8^(1/3) = 2.
What is the constant e?
The mathematical constant e is approximately 2.718281828.... It is the base of the natural logarithm and appears often in growth, decay, finance, probability, and calculus.
$$ e = \lim_{n\rightarrow \infty }\left ( 1+\frac{1}{n} \right )^{n}=2.71828\;18284\;59045\;23536... $$
