Find the Domain log base 6 of 5w

Problem

(log_6)(5*w)

Solution

1. Identify the condition for the domain of a logarithmic function. The argument of any logarithm must be strictly greater than zero.

2. Set up the inequality by taking the argument 5*w and setting it to be greater than zero.

5*w>0

3. Solve for w by dividing both sides of the inequality by 5

w>0

4. Express the domain in interval notation based on the inequality.

(0,∞)

Final Answer

Domain of *(log_6)(5*w)=(0,∞)

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