Home
Class 11
MATHS
The number of real values of the paramet...

The number of real values of the parameter `k` for which `(log_(16)x)^2-(log)_(16)x+(log)_(16)k=0` with real coefficients will have exactly one solution is `(1)`2 `(b)` 1 `(c)` 4 ` (d)` none of these

Text Solution

Verified by Experts

Let `log_16 x = y`
Then, given equation becomes,
`y^2-y+log_16 k = 0`
This is a quadratic equation and it has exactly one solution.
`:. D = 0`
`=>b^2-4ac = 0`
`=>(-1)^2 - 4(1)(log_16 k) = 0`
...
Promotional Banner

Topper's Solved these Questions

  • LINEAR INEQUALITIES

    CENGAGE|Exercise Solved Examples And Exercises|63 Videos
  • PERMUTATIONS AND COMBINATIONS

    CENGAGE|Exercise Solved Examples And Exercises|324 Videos

Similar Questions

Explore conceptually related problems

Solve log_(16)x+log_(4)x+log_(2)x=7

Solve : 3log_x(4)+ 2log_(4x)4+3log_(16x)4=0

The number of real solution(s) of the equation 9^(log_(3)(log_(e )x))=log_(e )x-(log_(e )x)^(2)+1 is equal to

Find the number of real solutions to the equation log_(0.5)x=|x| .

The value of 3^((log)_4 5)-5^((log)_4 3) is 0 (b) 1 (c) 2 (d) none of these

Number of real values of x satisfying the equation log_(x^2+6x+8)(log_(2x^2+2x+3)(x^2-2x))=0 is equal to

If log_2x+log_(4)x+log_(16)x=7/2 , find the value of x.

The number of integral solutions of log_(9)(x+1).log_(2)(x+1)-log_(9)(x+1)-log_(2)(x+1)+1lt0 is

The number of solutions of the equation log_(x+1)(x-0.5)=log_(x-0.5)(x+1) is

CENGAGE-LOGARITHM-Solved Examples And Exercises
  1. If x y^2=4a n d(log)3((log)2x)+(log)(1/3)((log)(1/2)y)=1,then x equals...

    Text Solution

    |

  2. x^(log5 x) > 5 implies x in

    Text Solution

    |

  3. The number of real values of the parameter k for which (log(16)x)^2-(...

    Text Solution

    |

  4. If S={x in R :((log)(0. 6)0. 216)(log)5(5-2x)lt=0}, then S is equal...

    Text Solution

    |

  5. If S={x in N :2+(log)2sqrt(x+1)>1-(log)(1/2)sqrt(4-x^2)} , then (a...

    Text Solution

    |

  6. Equation (log)4(3-x)+(log)(0. 25)(3+x)=(log)4(1-x)+(log)(0. 25)(2x+1)h...

    Text Solution

    |

  7. Solution set of the inequality 1/(2^x-1)>1/(1-2^(x-1)) is 1,oo) (b) 0...

    Text Solution

    |

  8. The solution set of the inequality (log)(10)(x^2-16)lt=(log)(10)(4x-11...

    Text Solution

    |

  9. Which of the following is not the solution of (log)x(5/2-1/x)> 1 (a...

    Text Solution

    |

  10. The equation x^((3/4)(log2 x)^2 + (log2 x) - (5/4))=sqrt(2) has (1)a...

    Text Solution

    |

  11. Solve the following equation of x : 2(log)x a+(log)(a x)a+3(log)(a^2x)...

    Text Solution

    |

  12. Solve for x :4^x-3^(x-1/2)=3^(x+1/2)-2^(2x-1)

    Text Solution

    |

  13. If P is the number of natural numbers whose logarithms to the base 10 ...

    Text Solution

    |

  14. Find the compound interest on Rs. 12000 for 10 years at the rate of 12...

    Text Solution

    |

  15. If x=(log)(2a)a , y=(log)(3a)2a ,z=(log)(4a)3a ,prove that 1+x y z=2y...

    Text Solution

    |

  16. Let L denote antilog32 0.6 and M denote the number of positive integer...

    Text Solution

    |

  17. Let x=(0. 15)^(20)dot Find the characteristic and mantissa of the loga...

    Text Solution

    |

  18. Using logarithms, find the value of 6.45 x 981.4

    Text Solution

    |

  19. In the 2001 census, the population of India was found to be 8. 7 * 10^...

    Text Solution

    |

  20. Given that "log"(10)2 = 0.30103, " log"(10) 3 = 0.47712 (approximatel...

    Text Solution

    |