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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: _ 14...

Paragraph: Consider a=log⁡23,b=log⁡35a=\log _2 3, b=\log _3 5 and c=log⁡57c=\log _5 7.Question: log⁡1463\log _{14} 63 equals:

Options

  1. Aab+cabc+1\frac{a b+c}{a b c+1}
  2. Babc+2aabc+1\frac{a b c+2 a}{a b c+1}
  3. Cbc+2abc+1\frac{b c+2}{a b c+1}
  4. Dnone of these

Correct answer

B. abc+2aabc+1\frac{a b c+2 a}{a 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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