Solve the equation for $x$. \[ \log _{16} 32=x \] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. $x=$ (Simplify your answer.) e. There is $m$ solition

Step 1 ：Convert the logarithmic equation into an exponential equation. The base of the logarithm becomes the base of the power, the right side of the equation becomes the exponent, and the number inside the logarithm becomes the result of the power. So, the equation \(\log _{16} 32=x\) can be rewritten as \(16^x = 32\).

Step 2 ：Simplify the equation to solve for \(x\).

Step 3 ：The solution provided includes complex solutions, which are not necessary in this context as we are looking for real solutions. The real solution is \(x = \frac{5}{4}\).

Step 4 ：Final Answer: \(x = \boxed{\frac{5}{4}}\)