Home
Class 12
MATHS
The product of roots of the equation (lo...

The product of roots of the equation `(log_8(8/x^2))/((log_8x)^2)=3` is 1 (b) (c) 1/3 (d) `1//4`

A

1

B

`1//2`

C

`1//3`

D

`1//4`

Text Solution

Verified by Experts

The correct Answer is:
D
Let ` log_(8) x = y`, then the given equation reduces to
` (1-2y)//y^(2) = 3`.
` rArr 3y^(2)+2y - 1 = 0`
`(3y-1)(y+1) = 0`
` rArr log_(8) x = y = 1//3, -1`
` rArr x = 2, 1//8`
Promotional Banner

Topper's Solved these Questions

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE|Exercise Exercise (Multiple)|17 Videos

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE|Exercise Exercise (Comprehension)|6 Videos

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE|Exercise Exercise 1.6|6 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

The number of roots of the equation (log)_(3sqrt("x"))x+(log)_(3x)sqrt(x)=0 is 1 (b) 2 (c) 3 (d) 0

The number of elements in set of all x satisfying the equation x^(log_3x^2+(log_3x)^2-10)=1/(x^2)i s (a)1 (b) 2 (c) 3 (d) 0

Number of real values of x satisfying the equation log_2(x^2-x)*log_2((x-1)/x)+(log_2x)^2=4 ,is (a) 0 (b) 2 (c) 3 (d) 7

The value of x for which the equation 5*3^(log_3x)-2^(1-log_2x)-3=0

Let a >1 be a real number. Then the number of roots equation a^(2(log)_2x)=15+4x^((log)_2a) is 2 (b) infinite (c) 0 (d) 1

For a >0,!=1, the roots of the equation (log)_(a x)a+(log)_x a^2+(log)_(a^2a)a^3=0 are given a^(-4/3) (b) a^(-3/4) (c) a (d) a^(-1/2)

The real solutions of the equation 2^(x+2). 5^(6-x)=10^x^2 is/are 1 (b) 2 (c) (log)_(10)(250) (d) (log)_(10)4-3

The number of solution of x^(log)x(x+3)^2=16 is a)0 (b) 1 (c) 2 (d) oo

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

The value of x satisfying the equation 3sqrt(5)^((log_5) 5^(((log)_5(log)_5log_5(x/2))) = 3 1 (b) 3 (c) 18 (d) 54

CENGAGE-LOGARITHM AND ITS PROPERTIES-Exercise (Single)
  1. If the equation 2^x+4^y=2^y is solved for y in terms of x where x<0, t...

    Text Solution

    |

  2. The number of solution of x^(log)x(x+3)^2=16 is a)0 (b) 1 (c) 2 (d...

    Text Solution

    |

  3. The product of roots of the equation (log8(8/x^2))/((log8x)^2)=3 is 1 ...

    Text Solution

    |

  4. Let a >1 be a real number. Then the number of roots equation a^(2(log)...

    Text Solution

    |

  5. The number of roots of the equation (log)(3sqrt("x"))x+(log)(3x)sqrt(x...

    Text Solution

    |

  6. The set of all x satisfying the equation x^(log)3x^2+((log)3x)^(2-10)=...

    Text Solution

    |

  7. Number of real values of x satisfying the equation (log)2(x^2-x)(log)...

    Text Solution

    |

  8. Find the value of x satisfying the equations log(3)(log(2)x)+log(1//3)...

    Text Solution

    |

  9. If x1a n dx2 are the roots of the equation e^2 x^(lnx)=x^3 with x1> x2...

    Text Solution

    |

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

    Text Solution

    |

  11. x^((log)5x)>5 implies x in (0,oo) (b) [2,2.5] (c) (2,2.5) (d) (0,2...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  15. If (log)2x+(log)2ygeq6, then the least value of x+y is 4 (b) 8 (d...

    Text Solution

    |

  16. Which of the following is not the solution log(x)(5/2-1/x) gt (5/2-1/x...

    Text Solution

    |

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

    Text Solution

    |

  18. Solution set of the inequality (log)(0. 8)((log)6(x^2+x)/(x+4))<0 is )

    Text Solution

    |

  19. Which of the following is not the solution of (log)3(x^2-2)<(log)3(3/2...

    Text Solution

    |

  20. The true solution set of inequality (log)((x+1))(x^2-4)>1 is equal to ...

    Text Solution

    |