Final answer:
The answer is B. No, since x = 0 does not satisfy the condition for the domain of the logarithmic functions in the equation, specifically that x must be greater than 3.
Step-by-step explanation:
The student asks if x = 0 is a valid potential solution to the equation log(x + 7) - log(x - 3) = 17. The direct answer is B. No.
In logarithmic equations, the arguments of the logarithm functions must be positive since the logarithm of a non-positive number is undefined. Therefore, for log(x + 7), x must be greater than -7, and for log(x - 3), x must be greater than 3. As x = 0 does not satisfy x > 3, it can not be a solution.
Step by step explanation:
- Consider the requirement for the domain of the logarithmic function: the argument must be positive, i.e., x + 7 > 0 and x - 3 > 0.
- Determine the smallest possible value for x that satisfies both conditions: x must be greater than 3.
- Conclude that since x = 0 does not meet the condition x > 3, it is not a valid solution.