Home
Class 11
MATHS
If a ,b ,a n dc are positive and 9a+3b+c...

If `a ,b ,a n dc` are positive and `9a+3b+c=90 ,` then the maximum value of `(loga+logb+logc)` is (base of the logarithm is 10).

Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    CENGAGE PUBLICATION|Exercise All Questions|9 Videos

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise All Questions|486 Videos

Similar Questions

Explore conceptually related problems

If a,b,c are positive real numbers and 2a+b+3c=1 , then the maximum value of a^(4)b^(2)c^(2) is equal to

If a and b are positive integer and a^2 - b^2 = 9 xx 11 then lets write the value of a & b

If a,b,c are positive real number, then the least value of (a+b+c)(1/a+1/b+1/c) is

If a, b, c are positive number satisfying 4ab + 6bc + 8ca = 9, then find the greatest value of (abc).

Let a ,b and c be real numbers such that a+2b+c=4 . Find the maximum value of (a b+b c+c a)dot

If A+B = 90^@ and tanA = 3/4 then the value of cotB is

If cot^(-1)n/pi>pi/6,n in N , then the maximum value of n is (a) 6 (b) 7 (c) 5 (d) none of these

If a ,b ,a n dc be in G.P. and a+x ,b+x ,and c+x in H.P. then find the value of x(a ,b and c are distinct numbers) .

If an a triangle A B C , a=3b and B-A=90^0, then find the value of tanA

If a ,b ,a n dc are positive and a+b+c=6, show that (a+1//b)^2+(b+1//c)^2+(c+1//a)^2geq75//4.

CENGAGE PUBLICATION-SEQUENCES AND SERIES-All Questions
  1. If x ,y in R^+ satisfying x+y=3, then the maximum value of x^2y is.

    Text Solution

    |

  2. For anyx ,y , in R^+,x y >0 . Then the minimum value of (2x)/(y^3)+(x...

    Text Solution

    |

  3. If a ,b ,a n dc are positive and 9a+3b+c=90 , then the maximum value o...

    Text Solution

    |

  4. Given that x ,y ,z are positive real such that x y z=32. If the minimu...

    Text Solution

    |

  5. If the product of n positive numbers is n^n , then their sum is (a)...

    Text Solution

    |

  6. If a,b,c are different positive real numbers such that b+c−a,c+a−b and...

    Text Solution

    |

  7. Find the greatest value of x^2 y^3, where x and y lie in the first qua...

    Text Solution

    |

  8. Find the maximum value of (7−x)^4 (2+x)^5 when x lies between −2 and ...

    Text Solution

    |

  9. If a1, a2,...... ,an >0, then prove that (a1)/(a2)+(a2)/(a3)+(a3)/(a4...

    Text Solution

    |

  10. If a > b and n is a positive integer, then prove that a^n-b^n > n(a b)...

    Text Solution

    |

  11. If a ,b ,a n dc are positive and a+b+c=6, show that (a+1//b)^2+(b+1/...

    Text Solution

    |

  12. Prove that [(x^2+y^2+z^2)/(x+y+z)]^(x+y+z)> x^x y^y z^z >[(x+y+z)/3]^(...

    Text Solution

    |

  13. Prove that 1^1xx2^2xx3^3xxxxn^nlt=[(2n+1)/3]^(n(n+1)/2),n in Ndot

    Text Solution

    |

  14. Prove that 2/(b+c)+2/(c+a)+2/(a+b)lt1/a+1/b+1/c ,where a ,b ,c>0.

    Text Solution

    |

  15. The minimum value of 2^(sin x) + 2^(cos x) is

    Text Solution

    |

  16. In how many parts an integer N>=5 should be divide so that the produc...

    Text Solution

    |

  17. In triangle ABC internal angle bisector AI,BI and CI are produced to m...

    Text Solution

    |

  18. The minimum value of (x^4+y^4+z^2)/(x y z) for positive real numbers x...

    Text Solution

    |

  19. If x ,y ,z are positive real number, then show that sqrt((x^(-1)y)xsqr...

    Text Solution

    |

  20. The least value of 6tan^2varphi+54cot^2varphi+18 is (I)54 when A.M.g...

    Text Solution

    |