Q22 / 60 · JEE Advanced 2013 (Paper 2) · Mathematics

If  3 x = 4 x - 1 , then x =

  • Correct answer
    A
    2 log 3 2 2 log 3 2 - 1
  • Correct answer
    B
    2 2 - log 2 3
  • Correct answer
    C
    1 1 - log 4 3
  • D
    2 log 2 3 2 log 2 3 - 1

Solution

3x = 4x - 1
x = (x - 1) log3 4
x ( 1 - 2 log3 2) = -2log3 2
x = 2 log 3 2 2 log 3 2 - 1
x log2 3 = (x - 1).2
x (log2 3 - 2) = -2
x = 2 2 - log 2 3
x = 1 1 - 1 2 log 2 3 = 1 1 - log 4 3

Hence, the correct answer is options: 'A', 'B', 'C'.

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