Find the Domain log base x of 3

Problem

(log_x)(3)

Solution

1. Identify the constraints for the base of a logarithm. For a logarithmic expression (log_b)(a) to be defined, the base b must be positive and not equal to 1

2. Apply the condition for the base being positive. In the expression (log_x)(3) the base is x so we must have x>0

3. Apply the condition for the base not being equal to 1 We must have x≠1

4. Identify the constraint for the argument of the logarithm. The argument a must be positive. Here, the argument is 3 and since 3>0 this condition is always satisfied.

5. Combine the inequalities x>0 and x≠1 to express the domain in interval notation.

Final Answer

Domain:(0,1)∪(1,∞)

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