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JEE Advanced 2013Paper 2
Exam
JEE Advanced
Year
2013
Paper
Paper 2
Subject
Mathematics
Chapter
Basics of Mathematics

JEE Advanced 2013 · Paper 2 · Mathematics · Basics of Mathematics

If 3 ^ x = 4 ^ x - 1 , then x =

If 3x=4x−1{3}^{\text{x}} = {4}^{\text{x} - 1}, then x =

Options

  1. A2 log322 log32−1\dfrac{{\text{2 log}}_{3} 2}{{\text{2 log}}_{3} 2 - 1}
  2. B\dfrac{2}{2 - {\text\log}_{2} 3}
  3. C\dfrac{1}{1 - {\text\log}_{4} 3}
  4. D2 log232 log23−1\dfrac{{\text{2 log}}_{2} 3}{{\text{2 log}}_{2} 3 - 1}

Correct answer

A. 2 log322 log32−1\dfrac{{\text{2 log}}_{3} 2}{{\text{2 log}}_{3} 2 - 1}

Step-by-step solution

3x = 4x - 1
x = (x - 1) log3 4
x ( 1 - 2 log3 2) = -2log3 2
\text{x} = \dfrac{2 {\text\log}_{3} 2}{2 {\text\log}_{3} 2 - 1}
x log2 3 = (x - 1).2
x (log2 3 - 2) = -2
\text{x} = \dfrac{2}{2 {- \text\log}_{2} 3}
\text{x} = \dfrac{1}{1 - \dfrac{1}{2} {\text\log}_{2} 3} = \dfrac{1}{1 - {\text\log}_{4} 3}
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