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.
Answer
The solution set is \( \boxed{\{0.03125\}} \)
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 \( \boxed{\{0.03125\}} \)
