Home
Class 12
MATHS
If log(y) x + log(x) y = 2, x^(2)+y = 12...

If `log_(y) x + log_(x) y = 2, x^(2)+y = 12` , then the value of xy is

A

9

B

12

C

15

D

21

Text Solution

Verified by Experts

The correct Answer is:
A
Let ` t=log_(y) x(x, y gt 0, and ne 1)," then " t+1/t = 2 or (t-1)^(2) = 0`
` :. T = log_(y) x = 1 , i.e., x = y `.We get
` x^(2) + x - 12 = 0 x = -4, 3`.
x = 3 only (-4 rejected)
` :. Y = 3`,
` :. X = 9`
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

if (log)_(y)x+(log)_(x)y=2,x^(2)+y=12, the value of xy is 9(b)12(c)15(d)30

If x and y satisfy the following system of equations, log x – log y = -2 , log x + 2 log y=1 then the value of xy is

If log_(y)x +log_(x)y = 7 , then the value of (log_(y)x)^(2) +(log_(x)y)^(2) , is

if log_(2)x+log_(2)y>=6 then the least value of x+y

If (log_(x)x)(log_(3)2x)(log_(2x)y)=log_(x^(x^(2)) , then what is the value of y ?

CENGAGE-LOGARITHM AND ITS PROPERTIES-Exercise (Single)
  1. The value of x satisfying the equation root(3)(5)^(log(5)5^(log(5)5^...

    Text Solution

    |

  2. If sqrt((log)2x)-0. 5=(log)2sqrt(x ,) then x equals

    Text Solution

    |

  3. If log(y) x + log(x) y = 2, x^(2)+y = 12 , then the value of xy is

    Text Solution

    |

  4. 4^(log9 3)+9^(log2 4)=1 0^(logx 83), then x is equal to

    Text Solution

    |

  5. Solve (x+1)^(log(10) (x+1))=100(x+1)

    Text Solution

    |

  6. If log2x+logx2=10/3=log2y+logy2 and x!=y ,then x+y=

    Text Solution

    |

  7. If (log)(10)[1/(2^x+x-1)]=x[(log)(10)5-1] , then x= 4 (b) 3 (c) 2 ...

    Text Solution

    |

  8. If (log)3{5+4(log)3(x-1)}=2, then x is equal to 4 (b) 3 (c) 8 (d) (...

    Text Solution

    |

  9. If 2x^(log(4)3)+3^(log(4)x)= 27, then x is equal to

    Text Solution

    |

  10. The equation log4(2-x)+log(0.25)(2+x)=log4(1-x)+log(0.25)(2x+1) has

    Text Solution

    |

  11. The values of b for which the equation 2log(1/25)(bx+28)=1log5(12-4x-x...

    Text Solution

    |

  12. If the equation 2^x+4^y=2^y is solved for y in terms of x where x<0, t...

    Text Solution

    |

  13. The number of solution of x^(log(x)(x+3)^(2)) = 16 is

    Text Solution

    |

  14. The product of roots of the equation (log(8)(8//x^(2)))/((log(8)x)^(2)...

    Text Solution

    |

  15. Let agt1 be a real number . If S is the set of real number x that are...

    Text Solution

    |

  16. the number of roots of the equation log(3sqrtx) x + log(3x) (sqrtx) =0...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  19. If xy^(2) = 4 and log(3) (log(2) x) + log(1//3) (log(1//2) y)=1 , then...

    Text Solution

    |

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

    Text Solution

    |