Problem 1 - Olympiad

To solve for x, we first notice that x = 0 results in 3^0 + 7^0 = 1 + 1 = 2. If we increase x, the sum will increase because both 3 and 7 are greater than 1, and raising them to a higher power will increase the sum. Similarly, if we decrease x, the sum will decrease because both 3 and 7 are greater than 1. So the value of x must be greater than 0. Then we notice that x = 1 is not a solution because 3^1 + 7^1 = 3 + 7 = 10. We realize that x must be between 0 and 1, but since x = 1 gives us the desired sum, x must actually be equal to 1. This makes the equation true, so the value of x in the equation is x = 1.