Step 1 :The question is asking for the solution to the equation \(f(x) = g(x)\). This means we need to find the value(s) of \(x\) for which the two functions \(f(x)\) and \(g(x)\) are equal. In other words, we need to solve the equation \(\frac{7}{3}x - 3 = 2^x - 4\) for \(x\).
Step 2 :This is a transcendental equation, which means it cannot be solved exactly using algebraic methods. However, it can be solved approximately using numerical methods.
Step 3 :The result from the numerical method is approximately 0. This means that the solution to the equation \(f(x) = g(x)\) is approximately 0. However, this is a numerical solution, so there may be some small error.
Step 4 :Final Answer: The solution to the equation \(f(x) = g(x)\) is approximately \(\boxed{0}\).