Home
Class 11
MATHS
If 0 le a le x, then the minimum value o...

If `0 le a le x`, then the minimum value of
`"log"_(a) x + "log"_(x) x` is

A

1

B

2

C

0

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
We have,
`0 le a le x`
`rArr "log"_(a) x ge 1`
`rArr "log"_(a) x + "log"_(x) x ge 1 + "log"_(x) x = 1 + 1 =2`
Promotional Banner

Topper's Solved these Questions

  • LOGARITHMS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|8 Videos

  • LOGARITHMS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|66 Videos

  • LOGARITHMS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|21 Videos

  • INEQUALITIES

    OBJECTIVE RD SHARMA ENGLISH|Exercise EXERCISE SECTION-II (Assertion-Reason )|1 Videos

  • MATRICES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|30 Videos

Similar Questions

Explore conceptually related problems

The minimum value of (x)/( log x) is

Statemen-1: If x lt 1 , then the least value of "log"_(2)x^(3) - "log"_(x) (0.125)" is "6 .

The maximum value of (log x)/( x) is

If f(x)=cos^(-1)(x^((3)/(2))-sqrt(1-x-x^(2)+x^(3))),AA 0 le x le 1 then the minimum value of f(x) is

For 0ltaltx , the minimum value of function log_a"" x+log_x a is 2.

For x > 1 , the minimum value of 2 log_10(x)-log_x(0.01) is

If g(x)=max(y^(2)-xy)(0le yle1) , then the minimum value of g(x) (for real x) is

Solve 2 log_(3) x - 4 log_(x) 27 le 5 .

If 0 le x le (pi)/(2) , then the number of value of x for which sin x - sin 2x + sin 3x = 0 , is

Let 1 le x le 256 and M be the maximum value of (log_(2)x)^(4)+16(log_(2)x)^(2)log_(2)((16)/(x)) . The sum of the digits of M is :

OBJECTIVE RD SHARMA ENGLISH-LOGARITHMS-Section I - Solved Mcqs
  1. If 0 le a le x, then the minimum value of "log"(a) x + "log"(x) x i...

    Text Solution

    |

  2. If a, b, c are positive real numbers, then a^("log"b-"log"c) xx b^(...

    Text Solution

    |

  3. The value of (bc)^log(b/c)*(ca)^log(c/a)*(ab)^log(a/b) is

    Text Solution

    |

  4. If x=(log)(2a)a , y=(log)(3a)2a ,z=(log)(4a)3a ,p rov et h a t1+x y z=...

    Text Solution

    |

  5. Evaluate : (1)/(log(a)bc + 1) + (1)/(log(b)ca + 1) + (1)/(log(c) ab ...

    Text Solution

    |

  6. If y=a^(1/(1-(log)a x))a n dz=a^(1/(1-(log)a y)),t h e np rov et h a t...

    Text Solution

    |

  7. If a = "log"2, b = "log" 3, c ="log" 7 " and " 6^(x) = 7^(x+4) then x=

    Text Solution

    |

  8. Given a^2+b^2=c^2&\ a .0 ; b >0; c >0,\ c-b!=1,\ c+b!=1,\ prove that ...

    Text Solution

    |

  9. If 5^x=(0. 5)^y=1000 , then 1/x-1/y=

    Text Solution

    |

  10. Solve for x :4^x3^(x-1//2)=3^(x+1//2)-2^(2x-1) .

    Text Solution

    |

  11. If (logx)/(2a+3b-5c)=(log y)/(2b+3c-5a)=(log z)/(2c=3a-5b') then xyz=

    Text Solution

    |

  12. I flogx=(logy)/2=(logz)/5, th ten x^4y^3z^(- 2)=

    Text Solution

    |

  13. If loga=1/2 logb=1/5logc then a^4b^3c^(-2)=

    Text Solution

    |

  14. If a=log(24)12,b=log(48)36 and c=log(36)24, abc is equal to

    Text Solution

    |

  15. If a,b,c are any three consecutive integers , prove that log(1+ac)=2lo...

    Text Solution

    |

  16. If ("log"(a)x)/("log"(ab)x) = 4 + k + "log"(a)b, "then" k=

    Text Solution

    |

  17. If a = 1 + log(x) yz, b = 1 + log(y) zx and c = 1 + log xy where x, ...

    Text Solution

    |

  18. (1)/("log"(2)n) + (1)/("log"(3)n) + (1)/("log"(4)n) + … + (1)/("log"(4...

    Text Solution

    |

  19. If n is a natural number such that n=P1^(a1)P2^(a2)P3^(a3)...Pk^(ak) ...

    Text Solution

    |

  20. Prove that number (log)2 7 is an irrational number.

    Text Solution

    |