1. The problem is to solve the equation $$7^x = 343$$ for the variable $x$. 2. We recognize that 343 is a power of 7. Specifically, $$343 = 7^3$$. 3. Using the property of exponents that if $$a^m = a^n$$ then $$m = n$$, we set the exponents equal: $$7^x = 7^3 \implies x = 3$$ 4. Therefore, the solution to the equation is $$x = 3$$. 5. Among the given options (3, 2, 5, 4), the correct answer is 3.