Solve for Exponents Calculator

What is Solve for Exponents?

Solving for exponents is the process of finding the power (exponent) to which a base number must be raised to obtain a given result. This is useful in various mathematical and real-world applications, including compound interest, population growth, and scientific calculations.

How to Calculate Solve for Exponents

To solve for exponents, we use logarithms. Logarithms allow us to convert exponential equations into linear equations, making it easier to solve for the unknown exponent.

Formula

The formula to solve for exponents is:

\[ n = \frac{\log(y)}{\log(x)} \]

Where:

• n is the exponent we're solving for
• x is the base
• y is the result

Calculation Steps

1. Start with the equation: \(x^n = y\)
2. Take the logarithm of both sides: \(\log(x^n) = \log(y)\)
3. Use the logarithm rule \(\log(a^b) = b \cdot \log(a)\): \(n \cdot \log(x) = \log(y)\)
4. Divide both sides by \(\log(x)\): \(n = \frac{\log(y)}{\log(x)}\)
5. Calculate the result using the values of x and y

Example

Let's solve for n in the equation \(2^n = 32\):

1. We have x = 2 and y = 32
2. Apply the formula: \(n = \frac{\log(32)}{\log(2)}\)
3. Calculate: n ≈ 5
4. Verify: \(2^5 = 32\)

Therefore, the exponent n is 5.