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

`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|7 Videos
  • DOT PRODUCT

    CENGAGE|Exercise DPP 2.1|15 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)

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

    Text Solution

    |

  4. (lim)(hvec0)((e+h)^(1n(e+h))-e)/hi s

    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)=0a n df^(prime)(0)=2, and let g(x)=f(-x+f(f(x)))dot ...

    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 coefficient 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))) Compute the value of f(50)dotf^(p...

    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 ...

    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

    |