 Online Calculators

# Solve for Exponents Calculator

Solve for the Exponent n
$x^n = y$

## Calculator Use

This calculator will solve for the exponent n in the exponential equation xn = y, stated x raised to the nth power equals y. Enter x and y and this calculator will solve for the exponent n using log().  Since taking the log() of negative numbers causes calculation errors they are not allowed.

## How to solve for exponents

For xn = y; solve for n by taking the log of both sides of the equation:

For:

$$x^n = y$$

Take the log of both sides:

$$\log_{}x^n = \log_{}y$$

By identity we get:

$$n \cdot \log_{}x = \log_{}y$$

Dividing both sides by log x:

$$n = \dfrac{\log_{}y}{\log_{}x}$$

### Find the exponent of a number

For the equation 3n = 81 where 3 is called the base and n is called the exponent, find the value of the exponent n using logarithms.

For:

$$3^n = 81$$

Take the log of both sides:

$$\log_{}3^n = \log_{}81$$

By identity we get:

$$n \cdot \log_{}3 = \log_{}81$$

Dividing both sides by log 3:

$$n = \dfrac{\log_{}81}{\log_{}3}$$

Using a calculator we can find that log 81 ≈ 1.9085 and log 3 ≈ 0.4771 then our equation becomes:

$$n = \dfrac{\log_{}81}{\log_{}3} \approx \dfrac{1.9085}{0.4771} \approx 4$$

Checking our answer 34 = 81.

Since taking the log() of negative numbers, 0 or 1 causes calculation errors we have provided some answers by definition and not actual calculations.

Cite this content, page or calculator as:

Furey, Edward "Solve for Exponents Calculator" at https://www.calculatorsoup.com/calculators/algebra/exponentsolve.php from CalculatorSoup, https://www.calculatorsoup.com - Online Calculators

Last updated: August 17, 2023