If x, y, z ∈ R^+ are such that z > y > x > 1 , {log y}x + {log ₓ}y = fr

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Basic of Logarithms

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If $x, y, z \in R^+$ are such that $z > y > x > 1$ , ${\log _y}x + {\log _x}y = \frac{5}{2}$ and ${\log _z}y + {\log _y}z = \frac{{10}}{3}$ then ${\log _x}z$ is equal to

A

$2$

B

$3$

C

$6$

D

$12$

Solution

$y=x^{2}, z=y^{3} \Rightarrow z=x^{6}$

$\log _{x} z=6$

Standard 11

Mathematics

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