Home
Class 12
MATHS
The value of x for which the sixth term ...

The value of `x` for which the sixth term in the expansion of `[2^(log)_2^sqrt(9^((x-1)_+7))+1/(2 ^(1/5)(log)_2(3^((x-1)_+1)))]^7` is 84 is

A

4

B

3

C

2

D

1

Text Solution

Verified by Experts

The correct Answer is:
C, D
`E = [sqrt(9^(x-1)+7) + (1)/((3^(r-1)+1)^(1//2))]^(7)`
Given, `T_(6) = 84`
`rArr .^(7)C_(5)(sqrt(9^(x-1)+7))^(7-5)((1)/((3^(x-1)+1^(1//5))))^(5) = 84`
`.^(7)C_(5)(9^(x-1)+7).(1)/((3^(x-1)+1)) = 84`
or `9^(x-1) + 7 = 4(3^(x-1)+1)`
or `3^(2x) - 12 . 3^(x) + 27 = 0`
or`(3^(x) -3)(3^(x) -9) = 0`
or `3^(x) = 3,9`
or `x = 1,2`
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE|Exercise Exercise (Comprehension)|20 Videos

  • BINOMIAL THEOREM

    CENGAGE|Exercise Matrix|4 Videos

  • BINOMIAL THEOREM

    CENGAGE|Exercise Exercise (Single)|90 Videos

  • AREA UNDER CURVES

    CENGAGE|Exercise Question Bank|10 Videos

  • CIRCLE

    CENGAGE|Exercise MATRIX MATCH TYPE|6 Videos

Similar Questions

Explore conceptually related problems

The largest value of x for which the fourth tem in the expansion (5^((2/5)(log)_5sqrt(4^(x)+44))+1/(5^(log_5) (2^((x-1)+7))^(1/3)))^8 is 336 is.

Solve: 1/4x^(log_2sqrt(x))=(2. x^((log)_2x))^(1/4)

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

The number of terms in the expansion of (1 + 5sqrt(2)x)^(9) + (1 - 5sqrt(2)x)^(9) is

Find the term independent of x in the expansion of (x^(2) - 1/x)^(7)

Find the number of nonzero terms in the expansion of (1+3sqrt(2)x)^9+(1-3sqrt(2)x)^9dot

If the 6th term in the expansion of (1/(x^(8/3))+x^2(log)_(10)x)^8 is 5600, then x equals

Find the value of (1/(49))^(1+(log)_7 2)+5^(-1(log)_((1/5))(7))

CENGAGE-BINOMIAL THEOREM-Exercise (Multiple)
  1. The value of x in the expression (x+x^((log)(10)))^5 if third term in ...

    Text Solution

    |

  2. The value of x for which the sixth term in the expansion of [2^(log)2^...

    Text Solution

    |

  3. If the 4th term in the expansion of (a x+1//x)^n is 5/2, then (a) a=1...

    Text Solution

    |

  4. In the expansion of (x+a)^n if the sum of odd terms is P and the sum o...

    Text Solution

    |

  5. If (4+sqrt(15))^n=I+f,w h r en is an odd natural number, I is an integ...

    Text Solution

    |

  6. If the coefficients of x^39 and x^40 are equal in the expansion of (p+...

    Text Solution

    |

  7. The sum of coefficient in the expansion of (1+a d-2x^2)^n is positive,...

    Text Solution

    |

  8. Let (1+x^2)^2(1+x)^n=sum(k=0)^(n+4)ak x^kdotIfa1,a2a n d a3 are in ari...

    Text Solution

    |

  9. For natural numbers m ,n ,if(1-y)^m(1+y)^n=1+a1y+a2y^2+ ,a n da1=a2=10...

    Text Solution

    |

  10. The middle term in the expansion of (x//2+2)^8 is 1120, then x in R i...

    Text Solution

    |

  11. In the expansion of (3-sqrt(17/4+3sqrt2))^15 the 11th term is a

    Text Solution

    |

  12. For the expansion (x sin p + x^(-1)cos p)^(10), (p in R),

    Text Solution

    |

  13. For which of the following values of x ,5t h term is the numerically g...

    Text Solution

    |

  14. Which of the following is/are true ?

    Text Solution

    |

  15. If sum(r=0)^nr/(^n Cr)=sum(r=0)^n(n^2-3n+3)/(2.^n Cr) , then a.n=1 b. ...

    Text Solution

    |

  16. The value of ^n C1+^(n+1)C2+^(n+2)C3++^(n+m-1)Cm is equal to ^m+n C(n-...

    Text Solution

    |

  17. If the number of terms in the expansion of (1-2/x+4/(x^(2))) x ne 0, i...

    Text Solution

    |

  18. In the expansion of (7^(1//3)+11^(1//9))^(6561) ,

    Text Solution

    |

  19. If (1 - x)^(n) = C(0) + C(1)x + C(2)x^(2) + ......... + C(n)x^(n), the...

    Text Solution

    |

  20. In the expansion of (a+b)^(n), if two consecutive terms are equal, the...

    Text Solution

    |