Home
Class 11
MATHS
Prove that (2^((log)2 1/4x)-3^((log)(27...

Prove that `(2^((log)_2 1/4x)-3^((log)_(27)(x^2+1)^3)-2x) /(7^(4(log)_(49)x)-x-1)>0`

Text Solution

Verified by Experts

`(2^(log_2^(1/4x))-3^(log_2^(x^2+1)^3)-2x)/(7^(4log_49^x)-x-1)>0`
`(2^(log_2^(x)^4)-3^(log_3^(x^2+1))-2x)/(7^(log_1^(sqrtx)^4)-x-1)`
`(x^4-(x^2+1)-2x)/(x^2-x-1)>0`
`(x^4-(x^2+2x+1))/(x^2-x-1)>0`
`((x^2)^2-(x+1)^2)/(x^2-x-1)>0`
`((x^2+x+1)(x^2-x-1))/(x^2-x-1)>0`
`x^2+x+1>0`
`(x+1/2)^2+3/4>0`
...
Promotional Banner

Topper's Solved these Questions

  • LINEAR INEQUALITIES

    CENGAGE PUBLICATION|Exercise All Questions|68 Videos

  • PERMUTATIONS AND COMBINATIONS

    CENGAGE PUBLICATION|Exercise All Questions|430 Videos

Similar Questions

Explore conceptually related problems

Solve: (log)_(0. 1)((log)_2((x^2+1)/(x-1))<0

Solve : 2(log)_3x-4(log)_x 27lt=5 (x >1)

Solve: (log)_(x+1/x)(log_2(x-1)/(x-2))>0

Solve (log)_2(x-1)> 4.

Solve 4^((log)_9x)-6x^((log)_9 2)+2^((log)_3 27)=0

Solve: (log)_2(4.3^x-6)-(log)_2(9^x-6)=1.

Prove that lim_(x rarr 2) log(2x-3)/(2(x-2))=1

Solve (log)_2(3x-2)=(log)_(1/2)x

Solve (log)_x2(log)_(2x)2=(log)_(4x)2.

Solve (log)_4 8+(log)_4(x+3)-(log)_4(x-1)=2.