Exponent Calculator

The calculator below can solve for either the final value of a variable x raised to an exponent n, or it can calculate an exponent n, given a variable X and a final value y.

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Exponents Formula

Xⁿ = Y

What are exponents?

An exponent is a term used in algebra to describe the factoring number in the algebraic equation shown above. Factoring is the process of multiplying a number by itself some number of times. For example, 2 raised to a factor of 2 (2²) is equal to 2 * 2 = 4. Another example is 3 raised to a factor of 4, which is equal to 3⁴ = 3*3*3*3 = 81. In these problems, the factor the original number is raised to is often referred to as the exponent n.

How to calculate an exponent?

The following example is similar to the ones described in the section above. This example will follow the calculation given the variable x and exponent n.

1. The fist step is to determine the values of both X and n. In this case, we will assume x=5 and n=3.
2. The next step is to set up the factor equation to solve for Y. This equation should look like the following, 5³ = Y.
3. The final step is to multiply 5 by itself 3 times, so 5*5*5 = 125.

This next example will show you how to calculate the exponent given the original variable X and the final value Y.

1. In this example let’s assume X = 8 and Y = 64.
2. The first step is to understand that a logarithm is the inverse of an exponent. Therefore, the exponent can be calculated using the log of Y with a base of X.
3. Finally solve the equation of n = log8(64)= 2.

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