Find the Domain

Problem

2*(log_2)(x)+3*(log_2)(2)=3*(log_2)(x)−(log_2)(1/32)

Solution

1. Identify the logarithmic terms in the equation that contain the variable x

2. Recall the definition of a logarithm (log_b)(g(x)) which requires the argument g(x) to be strictly greater than zero.

3. Set up the inequality for the argument of the first term 2*(log_2)(x) which is x>0

4. Set up the inequality for the argument of the third term 3*(log_2)(x) which is also x>0

5. Observe that the other terms, 3*(log_2)(2) and (log_2)(1/32) have constant positive arguments, so they do not impose additional restrictions on x

6. Combine the restrictions to determine the intersection of all conditions.

Final Answer

Domain:x>0

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