Find the Domain e natural log of 8x^5- natural log of 2x

Problem

ƒ(x)=ln(8*x5)−ln(2*x)

Solution

1. Identify the constraints for the natural logarithm function, which requires the argument to be strictly greater than zero.

2. Set up inequalities for each logarithmic term in the expression: 8*x5>0 and 2*x>0

3. Solve the first inequality 8*x5>0 by dividing by 8 which gives x5>0 and taking the fifth root, resulting in x>0

4. Solve the second inequality 2*x>0 by dividing by 2 which results in x>0

5. Determine the intersection of the two conditions x>0 and x>0 which is simply x>0

Final Answer

Domain:(0,∞)

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