If log(x + 4) = log(4) + log(x) and log(y + 6) = log(6), compare x and y.

Introduction / Context:
We solve two simple log equations independently and then compare the resulting values of x and y. The base is common (10 by default) and positivity of arguments must be ensured.

Given Data / Assumptions:

• log(x + 4) = log(4) + log(x) = log(4x).
• log(y + 6) = log(6).
• All log arguments are positive.

Concept / Approach:

• Use logarithm properties: log A + log B = log(AB).
• Since log is one-to-one on positive reals, equate arguments.

Step-by-Step Solution:

Verification / Alternative check:
Domain check: x + 4 > 0 and x > 0 (true for x = 4/3). For y, y + 6 > 0 (true for y = 0).

Why Other Options Are Wrong:

• x = y or x < y contradict the computed values.
• “Can’t say” is incorrect; both equations uniquely determine x and y.

Common Pitfalls:

• Using log(a) + log(b) = log(a + b), which is false.

Final Answer:
x > y