1. The problem is to solve the exponential equation $$7^x = 343$$ for the variable $x$. 2. Recall that $343$ can be expressed as a power of $7$ because $7^3 = 343$. 3. Rewrite the equation using this fact: $$7^x = 7^3$$ 4. Since the bases are the same and the function $7^x$ is one-to-one, the exponents must be equal: $$x = 3$$ 5. Therefore, the solution to the equation is $x = 3$. Final answer: $3$