Find the Domain log of x+9=1- log of x

Problem

(log_)(x+9)=1−(log_)(x)

Solution

1. Identify the logarithmic terms in the equation, which are (log_)(x+9) and (log_)(x)

2. Apply the definition of the domain for logarithmic functions, which requires the argument of every logarithm to be strictly greater than zero.

3. Set up inequalities for each argument: x+9>0 and x>0

4. Solve the first inequality by subtracting 9 from both sides to get x>−9

5. Solve the second inequality which is already simplified as x>0

6. Find the intersection of the two conditions x>−9 and x>0 which results in x>0

Final Answer

Domain:(0,∞)

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