Home
Class 12
MATHS
For positive real numbers a (a>1) let pa...

For positive real numbers `a (a>1)` let `p_a and q_a`, be the maximum and minimum values of `log_a(x)`, for `alt=xlt=2a` and if `p_a-q_a=1/2` then the value of a is not greater than

A

3

B

4

C

5

D

6

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE ENGLISH|Exercise High Level Problem|26 Videos

  • EQUATIONS

    RESONANCE ENGLISH|Exercise EXERCISE-2 (PART-II: PREVIOUSLY ASKED QUESTION OF RMO) |5 Videos

Similar Questions

Explore conceptually related problems

If p and q are positive real numbers such that p^2+q^2=1 , then the maximum value of p+q is

If p = log 20 and q = log 25, find the value of x, if 2 log(x + 1) = 2p - q.

If P=(1,1),Q=(3,2) and R is a point on x-axis then the value of PR+RQ will be minimum at

Let f(x) =x +(1)/(x). find local maximum and local minimum value of f(x) . Can you explain this discrepancy of locally minimum value being greater than locally maximum value.

If p and q are positive real numbers such that p^2+""q^2=""1 , then the maximum value of (p""+""q) is (1) 2 (2) 1/2 (3) 1/(sqrt(2)) (4) sqrt(2)

IF 10^(log_p{log_q(log_rx)}) =1 and log _q{log_r(log_px)}=0 . The value of q is

Find the value of : 2p + 3q + 4r + por when p =-1,q = 2 and r = 3

If p + q = 7 and pq = 12 , then will is the value of 1/(p^2) + 1/(q^2) ?

If 2009 = p^a x q^b where p and q are prime numbers, then the value of (p+q) is

If the sum of square of roots of the equation x^2+(p+i q)x+3i=0 is 8, then find the value of p and q , where p and q are real.

RESONANCE ENGLISH-DPP-QUESTION
  1. The vlaue of (81^((1)/(log(5)9))+3^((3)/(log(sqrt(6))3)))/(409)((sqrt(...

    Text Solution

    |

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

    Text Solution

    |

  3. For positive real numbers a (a>1) let pa and qa, be the maximum and mi...

    Text Solution

    |

  4. Let a >2 be a constant. If there are just 18 positive integers satisfy...

    Text Solution

    |

  5. If p,q in N" satisfy the equation "x^(sqrtx) = (sqrtx)^(x), then

    Text Solution

    |

  6. Which is/are true ? (A) log(0.2)3lt log(2)3 (B) log(sqrt(5))10ltlog (...

    Text Solution

    |

  7. The solution of the equation 7^(logx)-5^(logx+1)=3*5^(logx-1)-13*7 ^(l...

    Text Solution

    |

  8. Solve ((1)/(2))^(logx^(2))+2gt3.2^(log(-x))

    Text Solution

    |

  9. The values of x satisfying 2log((1)/(4))(x+5)gt(9)/(4)log((1)/(3sqrt(3...

    Text Solution

    |

  10. If a and b are positive integers such that a^(2)-b^(4)=2009, then a+b^...

    Text Solution

    |

  11. Find number of integral solutionlog(x+3)(x^(2)-x)lt1

    Text Solution

    |

  12. Suppose xy-5x+2y=30, where x and y are positive integers. Find the num...

    Text Solution

    |

  13. Solve : (i)" "((x-1)\(x-2)(x-3))/((x+1)(x+2)(x+3))" "(ii) " "(x^(4)+x...

    Text Solution

    |

  14. If alpha,beta be the roots of the equation (x-a)(x-b)+c=0(c!=0), then ...

    Text Solution

    |

  15. If sum(r=0)^(n-1)log(2)((r+2)/(r+1)) =prod(r=10)^(99)log(r) (r+1), the...

    Text Solution

    |

  16. Solve for x: log(2)x le 2/(log(2)x-1)

    Text Solution

    |

  17. Solve the in equality log(1/4) (2-x)>log(1/4) (2/(x+1)).

    Text Solution

    |

  18. Given that log(a^(2))(a^(2)+1)=16 find the value of log(a^(32))"("a+1/...

    Text Solution

    |

  19. If (3log(10)x+19)/(3log(10)x-1)=2 log(10)x+1, find solution of equatio...

    Text Solution

    |

  20. Prove that there exist no natural numbers, m and n such that m^(2)=n^(...

    Text Solution

    |