Question 51

Mathematics Logarithms Hard

If \( \log _{3} 2=x \& \log _{3} 5=y \) find \( \log _{3} 1620= \) ?

(A) \( 2(x+2)+y \)
(B) \( 2 x+y+2 \)
(C) \( 2(x+y)+1 \)
(D) None of these
✓ Correct Answer: Option A Verified Solution

📘 Step-by-Step Solution & Detailed Explanation:

Factorise: \(1620 = 4 \times 405 = 2^2 \times 3^4 \times 5\).

\(\log_3 1620 = 2\log_3 2 + 4\log_3 3 + \log_3 5 = 2x + 4 + y = 2(x+2) + y\)

Answer: (A)

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