Home
Class 12
MATHS
Find the solution of the inequality 2log...

Find the solution of the inequality `2log_(1/4)(x+5)>9/4log_(1/(3sqrt(3)))(9)+log_(sqrt(x+5))(2)`

A

`(-5,-4)`

B

`(-3,-1)`

C

`(-4,-1)`

D

`(-5,-2)`

Text Solution

Verified by Experts

The correct Answer is:
A, B
We have
`2log_((1)/(4))(x+5)gt(9)/(4)log_((1)/(3sqrt(3)))(9)+log_(sqrt(x+5))(2)`
`rArr -log_(2)(x+5)gt(9)/(4)(-(4)/(3))+(2)/(log_(2)(x+5))`
`rArr 3gt log_(2)(x+5)+(2)/(log_(2)(x+5))`
Let `log_(2)(x+5)=y`
`rArr 3 gt +(2)/(y)`
`rArr (y^(2)+2)/(y)-3lt 0`
`rArr (y^(2)-3y+2)/(y)ly 0`
`rArr ((y-2)(y-1))/(y)lt 0`
Using sign scheme method, we get
`y in (-oo,0)uu (1,2)`
`therefore log_(2)(x+5)in (-oo,0)uu(1,2)`
`therefore (x+5)in (2^(-oo),2^(0))uu(2^(1),2^(2))`
`therefore (x+5)in (0,1)uu(2,4)`
`therefore x in (-5,-4)uu (-3,-1)`
Promotional Banner

Topper's Solved these Questions

  • LOGARITHM AND ITS APPLICATIONS

    CENGAGE|Exercise Subjective Type|9 Videos

  • LINEAR COMBINATION OF VECTORS, DEPENDENT AND INDEPENDENT VECTORS

    CENGAGE|Exercise DPP 1.2|10 Videos

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE|Exercise JEE Previous Year|5 Videos

Similar Questions

Explore conceptually related problems

The solution set of the equation x^(log_x(1-x)^2)=9 is

The solution of the inequality (log)_(1/2sin^(-1)x >(log)_(1//2)cos^(-1)x is x in [(0,1)/(sqrt(2))] (b) x in [1/(sqrt(2)),1] x in ((0,1)/(sqrt(2))) (d) none of these

Find the sum of the squares of all the real solution of the equation 2log_((2+sqrt3)) (sqrt(x^2+1)+x)+log_((2-sqrt3)) (sqrt(x^2+1)-x)=3

The solution of the equation (log)_7(log)_5(sqrt(x+5)+sqrt(x)=0 is...

Solution set of the inequality (log)_(0. 8)((log)_6(x^2+x)/(x+4))<0 is )

The solution set of the inequality (log)_(10)(x^2-16)lt=(log)_(10)(4x-11) is 4,oo) (b) (4,5) (c) ((11)/4,oo) (d) ((11)/4,5)

Solve log_(3)(x+2)(x+4)+log_(1//3)(x+2) lt 1/2 log_(sqrt3)7 .

Find the value of (4/(log_(2)(2sqrt3))+2/(log_(3) (2sqrt3)))^(2) .

The number of real solution(s) of the equation 9^(log_(3)(log_(e )x))=log_(e )x-(log_(e )x)^(2)+1 is equal to

Find the value of the following: (i) log_(10) 2 + log_(10) 5 (ii) log_(3) (sqrt(11)-sqrt2) + log_(3) (sqrt11+sqrt2) (iii) log_(7) 35 - log_(7) 5