Solve the exponential equation by expressing each side as a power of the same base and then equating exponents. \[ 9^{\frac{x-2}{8}}=\sqrt{9} \] The solution set is Submit quiz

Step 1 ：The given equation is \(9^{\frac{x-2}{8}}=\sqrt{9}\).

Step 2 ：We can simplify the right side of the equation as \(9^{\frac{1}{2}}\).

Step 3 ：Now, we have the equation in the form \(9^{\frac{x-2}{8}}=9^{\frac{1}{2}}\).

Step 4 ：Since the bases are equal, the exponents must also be equal. Therefore, we can set up the equation \(\frac{x-2}{8}=\frac{1}{2}\) and solve for \(x\).

Step 5 ：Solving the equation gives us \(x = 6\).

Step 6 ：Final Answer: The solution to the equation is \(\boxed{6}\).