Explanation

Given the equation and solution path:

5^x + 2 - 5x = 600

If we interpret it as 5^(x+2) - 5^x = 600 (based on your calculation):

5^(2+2) - 5^2 = 5^4 - 5^2 = 625 - 25 = 600

This calculation implies x = 2 fits perfectly if the equation is treated as 5^(x+2) - 5^x = 600.

The value of x is 2.