1. **State the problem:** Find a formula to quickly determine the exponent $n$ such that $2^n = x$ for a given number $x$. 2. **Use logarithms:** The key formula is based on logarithms. If $2^n = x$, then taking the logarithm base 2 of both sides gives: $$n = \log_2 x$$ 3. **Explanation:** This formula means that to find the exponent $n$, you calculate the logarithm of $x$ with base 2. 4. **Using other logarithm bases:** If your calculator does not have a base 2 logarithm, use the change of base formula: $$n = \frac{\log_{10} x}{\log_{10} 2} \quad \text{or} \quad n = \frac{\ln x}{\ln 2}$$ where $\log_{10}$ is the common logarithm and $\ln$ is the natural logarithm. 5. **Example:** To find $n$ such that $2^n = 1024$: $$n = \log_2 1024 = \frac{\log_{10} 1024}{\log_{10} 2} = \frac{3.0103}{0.3010} = 10$$ **Final answer:** The formula to find the exponent quickly is $n = \log_2 x$, or using change of base $n = \frac{\log x}{\log 2}$.