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JEE Advanced
Exam
JEE Advanced
Subject
Mathematics
Chapter
Basics of Mathematics

JEE Advanced · Mathematics · Basics of Mathematics

Let x= (antilog_2 3) · _3 2, y= _2 ( _3( _2 512)) and z= _5 3 · _7...

Let x=x=\left(\operatorname{antilog}_2 3\right) \cdot \log _3 2, y=\log _2(log⁡3(log⁡2512))\left(\log _3\left(\log _2 512\right)\right) and z=log⁡53⋅log⁡75⋅log⁡27z=\log _5 3 \cdot \log _7 5 \cdot \log _2 7, then xyzx y z is equal to:

Correct answer

8

Step-by-step solution

x=8log⁡32,y=log⁡2(log⁡39)=1,z=log⁡53⋅log⁡75⋅log⁡27=log⁡23⇒xyz=8\begin{aligned} x & =8 \log _3 2, \\ y & =\log _2\left(\log _3 9\right)=1, \\ z & =\log _5 3 \cdot \log _7 5 \cdot \log _2 7=\log _2 3 \\ \Rightarrow \quad x y z & =8\end{aligned}
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