Question 45

Mathematics Function and Relation Hard

If x, y, z are three consecutive positive integers, then log (1 + xz) is

(A) log y
(B) <span class="math-tex">\(\log \dfrac{y}{2}\)</span>
(C) log (2y)
(D) 2 log (y)
✓ Correct Answer: Option D Verified Solution

📘 Step-by-Step Solution & Detailed Explanation:

Let \(x = y - 1\) and \(z = y + 1\).

\(1 + xz = 1 + (y-1)(y+1) = 1 + y^2 - 1 = y^2\)

\(\log(1 + xz) = \log y^2 = 2\log y\)

Answer: (D)

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