1. **State the problem:** Solve the equation $5^{2x} - 4 = 3f^x$ for $x$. 2. **Rewrite the equation:** The equation is $5^{2x} - 4 = 3f^x$. 3. **Express $5^{2x}$ as $(5^2)^x$:** $$5^{2x} = (5^2)^x = 25^x$$ 4. **Rewrite the equation using this:** $$25^x - 4 = 3f^x$$ 5. **Isolate terms:** $$25^x - 3f^x = 4$$ 6. **Note:** Without a specific value for $f$, the equation cannot be solved explicitly for $x$. 7. **If $f$ is known,** you can solve for $x$ by taking logarithms or using numerical methods. **Final answer:** The solution depends on the value of $f$. If $f$ is given, solve $$25^x - 3f^x = 4$$ for $x$ using logarithms or numerical methods.