Problem
Solve the logarithmic equation. Be sure to reject any value of $x$ that is not in the domain of the original logarithmic expression. \[ \log _{2} x=-5 \] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is $\{\quad\}$. (Type an exact answer in simplified form.) B. There is no solution.
Solution
Step 1 ：Convert the logarithmic equation to exponential form: \( x = 2^{-5} \)
Step 2 ：Solve for \( x \): \( x = 0.03125 \)
Step 3 ：Check the domain of the original logarithmic expression to ensure \( x \) is valid
Step 4 ：Since \( x > 0 \), the value \( x = 0.03125 \) is in the domain of the original logarithmic expression
Step 5 ：The solution set is \( \boxed{\{0.03125\}} \)
