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 ${}$ .
(Type an exact answer in simplified form.)
B. There is no solution.

Answer

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Answer

The solution set is ${0.03125}$

Steps

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 ${0.03125}$