Final answer:
To solve the equation 7^x = 3^x + 5, you can subtract 3^x from both sides to isolate the x term. Then, factor out the common term to simplify the equation. Finally, set the two sides equal to each other and solve for x.
Step-by-step explanation:
To find the solution to the equation 7^x = 3^x + 5, we can start by subtracting 3^x from both sides of the equation to isolate the x term on one side. This gives us 7^x - 3^x = 5. Next, we can factor out the common term, which is 3^x. This gives us 3^x(7^x/3^x - 1) = 5. Simplifying further, we get (7/3)^x - 1 = 5/3^x. Since we want to solve for x, we can set (7/3)^x - 1 equal to 5/3^x and solve the resulting equation.
To solve this equation, we can make a guess and check different values of x until we find the one that satisfies the equation. Based on the answer choices given, we can see that option (c) is the closest to the actual solution. However, the exact solution cannot be determined without using more advanced mathematical techniques like logarithms or numerical methods.