jee-main 2023 Q62

jee-main · India · session1_24jan_shift1 Laws of Logarithms Solve a Logarithmic Equation

For three positive integers $p , q , r , x ^ { p q ^ { 2 } } = y ^ { q r } = z ^ { p ^ { 2 } r }$ and $r = p q + 1$ such that 3, $3 \log _ { y } x , 3 \log _ { z } y , 7 \log _ { x } z$ are in A.P. with common difference $\frac { 1 } { 2 }$. The $r - p - q$ is equal to
(1) 2
(2) 6
(3) 12
(4) - 6

For three positive integers $p , q , r , x ^ { p q ^ { 2 } } = y ^ { q r } = z ^ { p ^ { 2 } r }$ and $r = p q + 1$ such that 3, $3 \log _ { y } x , 3 \log _ { z } y , 7 \log _ { x } z$ are in A.P. with common difference $\frac { 1 } { 2 }$. The $r - p - q$ is equal to\\
(1) 2\\
(2) 6\\
(3) 12\\
(4) - 6

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