Find the Domain log base 0.5 of x

Problem

(log_0.5)(x)

Solution

1. Identify the function type as a logarithmic function.

2. Recall the definition of a logarithm, which states that the argument of a logarithm must be strictly greater than zero.

3. Set up the inequality for the argument x to find the domain.

4. Solve the inequality x>0

5. Express the result in interval notation.

Final Answer

Domain of *(log_0.5)(x)=(0,∞)

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