Solve for Exponents Calculator

This calculator finds the exponent nn in the equation , where x is the base, nn is the exponent, and y is the result.

Simply input the values of x and y, and the calculator will compute nn using logarithms. Note that logarithms of negative numbers or zero are not allowed, as they result in errors.

How to Solve for Exponents

To solve the equation for n, follow these steps:

For:

x^n = y

Take the logarithm of both sides:

log(x^n) = log(y)

Using the logarithmic identity log(x^n) = n * log(x), we get:

n * log(x) = log(y)

Now, divide both sides by log(x):

n = log(y) / log(x)

For the equation 5^n = 125, where 5 is the base and nn is the exponent, we will calculate nn using logarithms.

Example: Finding the Exponent

For:

5^n = 125

Take the logarithm of both sides:

log(5^n) = log(125)

Using the identity, we get:

n * log(5) = log(125)

Now, divide both sides by log(5):

n = log(125) / log(5)

Using a calculator, we find that log(125) ≈ 2.0969 and log(5) ≈ 0.69897. Now substitute these values:

n = 2.0969 / 0.69897 ≈ 3

Checking our result, 5^3 = 125, confirming that n = 3.

Remember, logarithms of negative numbers, zero, or one are undefined, so these answers are based on identities rather than direct calculations.