Home
Class 12
MATHS
Prove that (2^(log(2^(1//4))x)-3^(log(27...

Prove that `(2^(log_(2^(1//4))x)-3^(log_(27)(x^(2)+1)^(3))-2x)/(7^(4log_(49)x)-x-1)gt0,AAx in(0,oo)`.

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

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

Let y=(2^(log_(2^(1//4))x)-3^(log_(27) (x^(2)+1)^(3))-2x)/(7^(4 log_(4 9)x)-x-1) and (dy)/(dx)=ax+b , the ordered pair (a, b) is

The ratio (2^(log_(2^(1/4))a)-3^(log_(27)(a^2+1)^3)-2a)/(7^(4log_(49)a-a-1)) simplfies to

Let y=(2^((log)_2 1/4x)-3^(log)_(27)(x^2+1)^3-2x)/(7^(4(log)_(49)x)-x-1)a n d(dy)/(dx)=a x+b , then the value of a+b is_______.

log_((1)/(2))log_(3)(x^(2)+5)+1<=0

(log_(2)x)^(2)+4(log_(2)x)-1=0

Solve :2(log)_(3)x-4(log)_(x)27 1)

log_(2)(4^(x)+4)=log_(2)2^(x)+log_(2)(2^(x+1)-3)

Solve 4^(log_(9)x)-6x^(log_(9)2)+2^(log_(3)27)=0 .