Home
Class 12
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^(log2^(1//4)x)-3^(log_(27)(x^(2)+1)^(3))-2x)/(7^(4log_(49)x)-x-1)`
`=(2^(log_(2)x^(4))-3^(log_(3)(x^(2)+1))-2x)/(7^(log_(7)x^(2))-x-1)`
`(x^(2)-(x^(2)+2x+1))/(x^(2)-x-1)`
`=x^(2)+x+1`
`(x+(1)/(2))^(2)+(3)/(4)gt0,AAx inR`
Promotional Banner

Topper's Solved these Questions

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE|Exercise Exercise 1.1|6 Videos

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE|Exercise Exercise 1.2|9 Videos

  • LOGARITHM AND ITS APPLICATIONS

    CENGAGE|Exercise Subjective Type|9 Videos

  • MATHMETICAL REASONING

    CENGAGE|Exercise JEE Previous Year|10 Videos

Similar Questions

Explore conceptually related problems

Solve: |x-1|^((log)_(10)x)^2-(log)_(10)x^2=|x-1|^3

(log x)/( (1 + log x)^(2))

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

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

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

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

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

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

Solve: 1/4x^(log_2sqrt(x))=(2. x^((log)_2x))^(1/4)