Find the Domain log base x of y=6

Problem

(log_x)(y)=6

Solution

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

2. Apply the condition for positivity to the base x This requires x>0

3. Apply the condition that the base cannot be 1 This requires x≠1

4. Identify the constraint for the argument of the logarithm. The argument y must be strictly positive.

5. Combine the constraints for x to define the domain of the function with respect to the base. In interval notation, this is (0,1)∪(1,∞)

Final Answer

Domain:{[x∈ℝ,x>0,x≠1]}

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