Find the Domain log of 40000/x=(12/20) log of 2

Problem

(log_)(40000/x)=12/20*(log_)(2)

Solution

1. Identify the logarithmic argument. For a logarithmic function (log_)(u) to be defined, the argument u must be strictly greater than zero.

2. Set up the inequality for the argument of the logarithm on the left side of the equation.

40000/x>0

3. Analyze the inequality. Since the numerator 40000 is a positive constant, the entire fraction is positive only if the denominator x is also positive.

x>0

4. Check for other restrictions. There are no other variables inside logarithms or denominators that would further restrict the domain.

5. Express the domain in interval notation.

(0,∞)

Final Answer

Domain:x∈(0,∞)

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