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JEE Advanced
Exam
JEE Advanced
Subject
Mathematics
Chapter
Basics of Mathematics

JEE Advanced · Mathematics · Basics of Mathematics

Paragraph: Consider a= _2 3, b= _3 5 and c= _5 7 . Question: Which...

Paragraph: Consider a=log⁡23,b=log⁡35a=\log _2 3, b=\log _3 5 and c=log⁡57c=\log _5 7.Question: Which of the following is incorrect?

Options

  1. Aabc<3a b c < 3
  2. Babc>2a b c>2
  3. Cabc<1a b c < 1
  4. Dabc<4a b c < 4

Correct answer

C. abc<1a b c < 1

Step-by-step solution

(i) log⁡1463=log⁡763log⁡714=1+log⁡79log⁡72+1=1+2bc1+1abc=abc+2aabc+1\log _{14} 63=\frac{\log _7 63}{\log _7 14}=\frac{1+\log _7 9}{\log _7 2+1}=\frac{1+\frac{2}{b c}}{1+\frac{1}{a b c}}=\frac{a b c+2 a}{a b c+1} (ii) abc=log⁡27⇒log⁡24<abc<log⁡28⇒2<abc<3\begin{aligned}& a b c=\log _2 7 \\ & \Rightarrow \quad \log _2 4 < a b c < \log _2 8 \\ & \Rightarrow \quad 2 < a b c < 3 \end{aligned}
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