Find the Domain log of 500/3+ log base 6 of x

Problem

(log_)(500/3)+(log_6)(x)

Solution

1. Identify the components of the expression. The first term (log_)(500/3) is a constant, while the second term (log_6)(x) contains the variable x

2. Recall the definition of the domain for logarithmic functions. For any expression (log_b)(u) the argument u must be strictly greater than zero.

3. Analyze the first term. Since 500/3>0 the first term is defined for all real numbers x

4. Set up the inequality for the second term. The argument of (log_6)(x) is x so we must satisfy the condition x>0

5. Determine the intersection of the conditions. The expression is defined only when x is positive.

Final Answer

Domain:(0,∞)

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