Home
Class 12
MATHS
There exists a positive number k such th...

There exists a positive number k such that ` log_2x+ log_4x+ log_8x= log_kx`, for all positive real no x. If k=`a^(1/b)` where (a,b) `epsilon` N, the smallest possible value of (a+b)= (C) 12 A) 75 (B) 65 (D) 63_

A

12

B

63

C

65

D

75

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • LOGARITHM AND THEIR PROPERTIES

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|9 Videos

  • LOGARITHM AND THEIR PROPERTIES

    ARIHANT MATHS|Exercise Exercise (Passage Based Questions)|12 Videos

  • LOGARITHM AND THEIR PROPERTIES

    ARIHANT MATHS|Exercise Exercise For Session 3|5 Videos

  • LIMITS

    ARIHANT MATHS|Exercise Exercise For Session 6|4 Videos

  • MATHEMATICAL INDUCTION

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|2 Videos

Similar Questions

Explore conceptually related problems

There exists a positive number k such that log_(2)x+log_(4)x+log_(8)x=log_(k)x, for all positive real no x.If k=a^((1)/(b)) where (a,b)varepsilon N, the smallest possible value of (a+b)=(C)12 A) 75 (B) 65 (D) 63_(-)

If k in N, such that log_(2)x+log_(4)x+log_(8)x=log_(k)x!=1 then the value of k is

If x is a positive real number different from 1 such that log_(a)x,log_(b)x,log_(c)x are in A.P then

If X is a positive real number other than 1 such that log_(a)x.log_(b)x,log_(c)x are in A.P. then

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 is a positive real number different from unity such that 2log_(b)x=log_(a)x+log_(c)x then prove that c^(2)=(ca)^(log_(a)b)

Let x and y be positive numbers such that log_(9)x=log_(12)y=log_(16)(x+y) where x

Suppose log_(a)b+log_(b)a=c . The smallest possible integer value of c for all a, b gt 1 is -

If a, b, c, are positive real numbers and log_(4) a=log_(6)b=log_(9) (a+b) , then b/a equals

Suppose log_(a)b+log_(b)a=c. The smallest possible integer value of c for all a,b>1 is

ARIHANT MATHS-LOGARITHM AND THEIR PROPERTIES-Exercise (Single Option Correct Type Questions)
  1. If log(10)2=0.3010..., the number of digits in the number 2000^(2000)...

    Text Solution

    |

  2. There exists a positive number k such that log2x+ log4x+ log8x= logkx...

    Text Solution

    |

  3. If x1,x2 & x3 are the three real solutions of the equation x^(log10^2...

    Text Solution

    |

  4. If f(n)=prod(i=2)^(n-1)logi(i+1), the value of sum(k=1)^100f(2^k) equa...

    Text Solution

    |

  5. If log(3)27.logx7=log(27)x.log(7)3, the least value of x is

    Text Solution

    |

  6. If x=log5(1000) and y=log7(2058),then

    Text Solution

    |

  7. Solve for x log5 120 + (x - 3) - 2*log5 (1- 5^(x - 3)) = - log5 (0.2 ...

    Text Solution

    |

  8. If xn > x(n-1) > ..........> x3 > x1 > 1. then the value of log(x1) [...

    Text Solution

    |

  9. If (x(y+z-x))/(logx)=(y(z+x-y))/(logy)(z(x+y-z))/(logz),p rov et h a ...

    Text Solution

    |

  10. If y=a^(1/(1-logax)), z=a^(1/(1-logay)) then prove that x=a^(1/(1-loga...

    Text Solution

    |

  11. If (log)(0. 3)(x-1)<(log)(0. 09)(x-1), then x lies in the interval (2,...

    Text Solution

    |

  12. The value of a^x-b^y is (wherex=sqrt(logab)and y=sqrt(logba),agt0,bgt0...

    Text Solution

    |

  13. If x=1+log(a) bc, y=1+log(b) ca, z=1+log(c) ab, then (xyz)/(xy+yz+zx) ...

    Text Solution

    |

  14. The value of a^((logb(logbx))/(logb a)), is

    Text Solution

    |

  15. Find the value of 49^((1-log7(2)))+5^(-log5(4) is

    Text Solution

    |

  16. The number of real values of the parameter k for which the equation ("...

    Text Solution

    |

  17. The number of roots of the equation x^(logX(x+3)^2)=16 is

    Text Solution

    |

  18. The point on the graph y=log2log6{2^sqrt(2x+1)+4} whose y coordinate i...

    Text Solution

    |

  19. Given ,log2=0.301 and log3=0.477, then the number of digits before dec...

    Text Solution

    |

  20. The values of x, satisfying the equation for AA a > 0, 2log(x) a + lo...

    Text Solution

    |