Solve for x in the equation \(5^{x} \times 5^{x + 1} = 25\).

Answer Details

To solve the equation \(5^{x} \times 5^{x + 1} = 25\), we can use the rules of exponents. Since the bases are the same (both are 5), we can add the exponents to get: $$5^{x} \times 5^{x + 1} = 5^{2}$$ $$5^{2x + 1} = 5^{2}$$ Now we can solve for x by equating the exponents: $$2x + 1 = 2$$ $$2x = 1$$ $$x = \frac{1}{2}$$ Therefore, the solution is \(\frac{1}{2}\).