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 \(\frac{1}{2}\).