Home
Class 11
MATHS
Solve 4^((log)9x)-6x^((log)9 2)+2^((log)...

Solve `4^((log)_9x)-6x^((log)_9 2)+2^((log)_3 27)=0`

Text Solution

Verified by Experts

`4^(log_9x) - 6x^(log_9 2)+2^(log_3 27) = 0`
`=>4^(log_9x) - 6*2^(log_9 x) +2^(log_3 2^3) = 0`
Let `2^(log_9 x) = t`,
Then,
`=>t^2 -6t +8 = 0`
`=>t^2-4t-2t+8 = 0`
`=>(t-4)(t-2) = 0`
`=>t = 2 or t = 4`
...
Promotional Banner

Topper's Solved these Questions

  • LINEAR INEQUALITIES

    CENGAGE PUBLICATION|Exercise All Questions|68 Videos

  • PERMUTATIONS AND COMBINATIONS

    CENGAGE PUBLICATION|Exercise All Questions|430 Videos

Similar Questions

Explore conceptually related problems

Solve : 6((log)_x2-(log)_4x)+7=0.

Solve (log)_x2(log)_(2x)2=(log)_(4x)2.

Solve (log)_(2x)2+(log)_4 2x=-3//2.

Solve (log)_(2x)2+(log)_4 2x=-3//2.

Solve for: x :(2x)^((log)_b2)=(3x)^((log)_b3) .

Solve x^((log)_y x)=2a n dy^((log)_x y)=16

Solve x^((log)_y x)=2 and y^((log)_x y)=16

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

Solve (log)_2(x-1)> 4.

Find the value of ((log)_3 4)((log)_4 5)((log)_5 6)((log)_6 7)((log)_7 8)((log)_8 9)dot

CENGAGE PUBLICATION-LOGARITHM-All Questions
  1. Solve 4^(log(2)log(x))=logx-(logx)^(2)+1 (base is e).

    Text Solution

    |

  2. Solve: 4(log)(x/2)(sqrt(x))+2(log)(4x)(x^2)=3(log)(2x)(x^3)dot

    Text Solution

    |

  3. Solve 4^((log)9x)-6x^((log)9 2)+2^((log)3 27)=0

    Text Solution

    |

  4. Solve: 1/4x^(log2sqrt(x))=(2. x^((log2x)))^(1/4)dot

    Text Solution

    |

  5. Solve |x-1|^((log(10) x)^2-log(10) x^2=|x-1|^3

    Text Solution

    |

  6. Solve (log)2(x-1)> 4.

    Text Solution

    |

  7. Solve (log)3(x-2)lt=2.

    Text Solution

    |

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

    Text Solution

    |

  9. If x y^2=4a n d(log)3((log)2x)+(log)(1/3)((log)(1/2)y)=1,t h e nxe q u...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  17. Which of the following is a solution of (logx)(5/2-1/x) gt (5/2-1/x) ?

    Text Solution

    |

  18. Solve x^[[3/4(log2 x)^2+log2 x-5/4]] = sqrt2

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |