Home
Class 12
MATHS
Solve log(3x -2) x^(2) gt log (3x-2) (...

Solve ` log_(3x -2) x^(2) gt log _(3x-2) (3x -2)`

Text Solution

Verified by Experts

We have ,
` log_(3x -2) x^(2) gt log _(3x-2) (3x -2)`
`rArr {{:(x^(2) gt 3x -2, 3x - 2 gt 1),(x^(2) lt 3x - 2 , 0 lt 3x - 2 lt 1):}`
`rArr {{:(x^(2) gt 3x +2gt0, x gt 1),(or ),(x^(2) lt 3x + 2 lt 0,(2)/(3)lt xlt 1):}`
` rArr {{:((x -2) (x-1) gt 0, x gt 1 ),(or),((x-2)(x-1) lt 0 , (2)/(3) lt x lt 1 ):}`
`rArr {{:(x gt 2 or x lt 1 ,, x gt 1 ),(1 lt x lt 2 ,,(2)/(3) lt x lt 1):}`
`rArr {{:(x gt 2 as x gt 1 rArr x cancel lt 1 ),("no x exists in (1, 2)s.t". (2)/(3)lt x lt 1):}`
` rArr x in (2, oo)`
Promotional Banner

Topper's Solved these Questions

  • SEQUENCES AND SERIES

    AAKASH INSTITUTE|Exercise Try Yourself|85 Videos

  • SEQUENCES AND SERIES

    AAKASH INSTITUTE|Exercise Assignment (SECTION - A) One option is correct|60 Videos

  • RELATIONS AND FUNCTIONS

    AAKASH INSTITUTE|Exercise Assignment (Section - J) Aakash Challengers Questions|8 Videos

  • SETS

    AAKASH INSTITUTE|Exercise SECTION-I(Aakash Challengers Questions)|5 Videos

Similar Questions

Explore conceptually related problems

Solve log_(3)(x-2)<=2

Solve log_(3)|x|gt 2 .

Solve log_(3)(x-2) le 2 .

Solve log_(x-2)(3x^2-x-1)>0 .

Solve for x:(a) log_(0.3)(x^(2)+8) gt log_(0.3)(9x) , b) log_(7)( (2x-6)/(2x-1)) gt 0

Solve log_(2).(x-1)/(x-2) gt 0 .

Solve : log_(1-2x)(6x^(2)-5x+1)-log_(1-3x)(4x^(2)-4x+1)=2

Solve the equation log(3x^(2)+x-2)=3log(3x-2) .

Solve: log_(3)(2x^(2)+6x-5)>1