Question

Is x = 0 a valid potential solution to the equation log(x + 7) - log(x - 3) = 17?

A. Yes
B. No
C. Maybe
D. Undefined

Answer 1

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:

1. Consider the requirement for the domain of the logarithmic function: the argument must be positive, i.e., x + 7 > 0 and x - 3 > 0.
2. Determine the smallest possible value for x that satisfies both conditions: x must be greater than 3.
3. Conclude that since x = 0 does not meet the condition x > 3, it is not a valid solution.