Home
Class 11
MATHS
If xa n dy are real numbers such that 2...

If `xa n dy` are real numbers such that `2log(2y-3x)=logx+logy` ,then find `x/y`.

Text Solution

Verified by Experts

`2log(2y-3x)=logx+logy`
`log(2y-3x)^2=logxy`
`(2y-3x)^2=xy`
`y^2[2-3x/y]^2=xy`
`4+9(x/y)^2-12x/y=x/y`
Let `x/y=t`
`4+9t^2-12t-t=0`
`9t^2-13t+4=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

If x and y are positive real numbers such that 2log(2y - 3x) = log x + log y," then find the value of " x/y .

If x and y are real numbers such that 16^(x^(2)+y)+16^(x+y^2)=1 , then find the values of x and y.

The x , y , z are positive real numbers such that (log)_(2x)z=3,(log)_(5y)z=6,a n d(log)_(x y)z=2/3, then the value of (1/(2z)) is ............

Suppose xa n dy are real numbers and that x^2+9y^2-4x+6y+4=0 . Then the maximum value of ((4x-9y))/2 is__________

If log ((x+y)/3)=1/2 (log x +log y) then find the value of x/y+y/x

If x^2 + y^2 = 6xy , prove that 2 log (x + y) = logx + logy + 3 log 2

Let z=x+i y be a complex number, where xa n dy are real numbers. Let Aa n dB be the sets defined by A={z :|z|lt=2}a n dB={z :(1-i)z+(1+i)bar z geq4} . Find the area of region AnnB

Let xa n dy be two real variable such that x >0a n dx y=1 . Find the minimum value of x+y .

Let f be a function satisfying of xdot Then f(x y)=(f(x))/y for all positive real numbers xa n dydot If f(30)=20 , then find the value of f(40)dot

CENGAGE-LOGARITHM-Solved Examples And Exercises
  1. The value of 5^((log)(1/5)(1/2))+(log)(sqrt(2))4/(sqrt(7)+sqrt(3))+(lo...

    Text Solution

    |

  2. The value of N=((log)5 250)/((log)(50)5)-((log)5 10)/((log)(1250)5) is...

    Text Solution

    |

  3. If xa n dy are real numbers such that 2log(2y-3x)=logx+logy ,then fin...

    Text Solution

    |

  4. If loge((a+b)/2)=1/2(loge a+loge b), then find the relation between a ...

    Text Solution

    |

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

    Text Solution

    |

  6. The value of loga b-log|b|= (a)loga (b) "log"|a| (c) -loga (d) ...

    Text Solution

    |

  7. If (21. 4)^a=(0. 00214)^b=100 , then the value of 1/a-1/b is 0 (b) 1 ...

    Text Solution

    |

  8. Given that log(2)=0. 3010 , the number of digits in the number 2000^(...

    Text Solution

    |

  9. The number of N=6-(6(log)(10)2+(log)(10)31) lies between two successi...

    Text Solution

    |

  10. (log)4 18 is (a) a rational number (b) an irrational number (c) ...

    Text Solution

    |

  11. Solve: (log)((2x+3))(6x^2+23x+21)+(log)((3x+7))(4x^2+12 x+9)=4

    Text Solution

    |

  12. Given aa n db are positive numbers satisfying 4(log(10)a)^2+((log)2b)...

    Text Solution

    |

  13. If ((log)a N)/((log)c N)=((log)a N-(log)b N)/((log)b N-(log)c N),w h e...

    Text Solution

    |

  14. If (log)b a(log)c a+(log)a b(log)c b+(log)a c(log)bc=3 (where a , b ,...

    Text Solution

    |

  15. Solve for: x :(2x)^((log)b2)=(3x)^((log)b3) .

    Text Solution

    |

  16. Let a=(log)3(log)3 2. An integer k satisfying 1<2^(-k+3^((-a)))<2, mus...

    Text Solution

    |

  17. The value of 6+(log)(3/2)[1/(3sqrt(2)) * sqrt{ (4 - 1/(3sqrt(2))) sqr...

    Text Solution

    |

  18. (log)(x-1)x (log)(x-2)(x-1) (log)(x-12)(x-11)=2,x is equal to: 9 (b) ...

    Text Solution

    |

  19. If f(x)=log((1+x)/(1-x)),t h e n (a)f(x1)f(x)=f(x1+x2) (b)f(x+...

    Text Solution

    |

  20. If a , b , c are consecutive positive integers and (log(1+a c)=2K , ...

    Text Solution

    |