Home
Class 12
MATHS
Prove that (2^(log2^(1//4)x)-3^(log(27)(...

Prove that `(2^(log2^(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

`y=(x^(4)-(x^(2)+2x+1))/(x^(2)-x-1)=x^(2)+x+1`
`therefore" "(dy)/(dx)=2x+1=ax +b`
Hence, a=2 and b=1
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    CENGAGE|Exercise JEE Previous Year|15 Videos

  • DIFFERENTIATION

    CENGAGE|Exercise Multiple Correct Answers Type|3 Videos

  • DIFFERENTIATION

    CENGAGE|Exercise Exercise (Matrix)|5 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise Question Bank|25 Videos

  • DOT PRODUCT

    CENGAGE|Exercise DPP 2.1|15 Videos

Similar Questions

Explore conceptually related problems

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) .

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)

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

CENGAGE-DIFFERENTIATION-Exercise (Numerical)
  1. If function f satisfies the relation f(x)xf^(prime)(-x)=f(-x)xf^(prime...

    Text Solution

    |

  2. If y=(a+b x^(3/2))/(x^(5/4))a n dy^(prime)=0a tx=5, then the value o...

    Text Solution

    |

  3. Prove that (2^(log2^(1//4)x)-3^(log(27)(x^(2)+1)^(3))-2x)/(7^(4log(49)...

    Text Solution

    |

  4. lim(h to 0) ((e+h)^(In(e+h))-e)/(h) is-

    Text Solution

    |

  5. If the function f(x)=-4e^((1-x)/2)+1+x+(x^2)/2+(x^3)/3a n dg(x)=f^(-1)...

    Text Solution

    |

  6. Suppose that f(0)=0 and f'(0)=2, and let g(x)=f(-x+f(f(x))). The value...

    Text Solution

    |

  7. f(x) is polynomial of degree 4 with real coefficients such that f(x)=0...

    Text Solution

    |

  8. A nonzero polynomial with real coefficients has the property that f(x)...

    Text Solution

    |

  9. A function is reprersented parametrically by the equations x=(1+t)/(t^...

    Text Solution

    |

  10. Let z=(cosx)hat5a n dy="sin"xdot Then the value of 2(d^2z)/(dy^2)a tx=...

    Text Solution

    |

  11. Let g(x)={(x^2+xtanx-xtan2x)/(a x+tanx-tan3x),x!=0 0,x=0 If g^(prime)...

    Text Solution

    |

  12. "Let "f(x)=x + (1)/(2x + (1)/(2x + (1)/(2x + .....oo))). Then the v...

    Text Solution

    |

  13. Let F(x)=f(x)g(x)h(x) for all real x ,w h e r ef(x),g(x),a n dh(x) are...

    Text Solution

    |

  14. "If "y=(root(3)(1+3x)root(4)(1+4x)root(5)(1+5x))/(root(7)(1+7x)root(8)...

    Text Solution

    |

  15. f^(prime)(x)=varphi^(prime)(x)=f(x) for all xdot Also, f(3)=5a n df^(p...

    Text Solution

    |

  16. If y=f(x) is an odd differentiable function defined on (-oo,oo) such t...

    Text Solution

    |

  17. If x^3+3x^2-9x+c is of the form (x-alpha)^2(x-beta) then c is equal to

    Text Solution

    |

  18. If graph of y=f(x) is symmetrical about the point (5,0) and f^(prime)(...

    Text Solution

    |

  19. Let f(x)=(x-1)(x-2)(x-3)(x-n),n in N ,a n df(n)=5040. Then the value ...

    Text Solution

    |

  20. y=f(x) , where f satisfies the relation f(x+y)=2f(x)+x y(y)+ysqrt(f(x)...

    Text Solution

    |