Home
Class 12
MATHS
Show that |[1,logab,logac],[logba,1,logb...

Show that `|[1,log_ab,log_ac],[log_ba,1,log_bc],[log_ca,log_cb,1]|=0`,(a>0,b>0,c>0)

Promotional Banner

Topper's Solved these Questions

  • HIGHER SECONDARY EXAMINATION 2019

    UNITED BOOK HOUSE|Exercise Exercise|20 Videos

  • HIGHER SECONDARY QUESTION 2018

    UNITED BOOK HOUSE|Exercise EXERCISE|44 Videos

Similar Questions

Explore conceptually related problems

Prove that |[1,log_xy,log_xz],[log_yx,1,log_yz],[log_zx,log_zy,1]|=0

Prove that , |[1,log_x^y,log_x^z],[log_y^x,1,log_y^z],[log_z^x,log_z^y,1]|=0

Show that log_(2)log_(2)log_(2) 16=1

prove that, |{:(" "1,log_xy,log_xz),(log_yx," "1,log_yz),(log_zx,log_zy," "1):}|=0

Show that log_(3)log_(2)log_(sqrt3)81 = 1

Show that log_(b)a xx log_(c )b xx log_(d)c = log_(d)a .

|{:(log_x xyz,log_xy,log_xz),(log_yxyz,1,log_yz),(log_zxyz,log_zy,1):}|=0

If x, y and z be greater than 1, then the value of |(1,log_(x)y,log_(x)z),(log_(y)x,1,log_(y)z),(log_(z)x,log_(z)y,1)| is

Show that (1)/(log_(a)bc+1)+(1)/(log_(b)ca+1)+(1)/(log_(c )ab+1)=1

If a,b,c be three distinct positive numbers, each different from 1 such that ("log"_ba"log"_ca-"log"_aa)+("log"_ab"log"_cb-"log"_b b)+("log"_ac"log"_bc-"log"_c c)=0 , then prove that abc=1

UNITED BOOK HOUSE-HIGHER SECONDARY EXAMINATION 2020.-EXERCISE
  1. The principal value of sin^(-1)(sin((5pi)/6))is-

    Text Solution

    |

  2. Evaluate : sec^2(tan^(-1)2)+cosec^2(cot^(-1)3).

    Text Solution

    |

  3. Show that |[1,logab,logac],[logba,1,logbc],[logca,logcb,1]|=0,(a>0,b>0...

    Text Solution

    |

  4. Find the deferential equation of xy= Ae^x+Be^(-x)+x^2 by eleminating A...

    Text Solution

    |

  5. If x^2 = a^(sin^(-1)t) and y^2= a^(cos^(-1)t) then show that (dy)/(dx)...

    Text Solution

    |

  6. If f(x) = (sin 5x)/(2x) (when x!=0) = (5k)/4(when x= 0), and f(x) is...

    Text Solution

    |

  7. If x>0,y>0 and xy= 100, find the minimum value of (x+y)

    Text Solution

    |

  8. Evaluate: int((cosx+xsinx)/(x(x+cosx)))dx.

    Text Solution

    |

  9. If f(x) = -f(-x) then show that overset(a)underset(-a)int f(x)dx =0.

    Text Solution

    |

  10. Find a vector of magnitude 14 in the direction of the vector -3hat i+6...

    Text Solution

    |

  11. Find the direction cosines of a straight line which is situate on yz-p...

    Text Solution

    |

  12. If P(A)=1/4,P(B)=1/3 and P(A-B)=1/6 then verify whether a and B are tw...

    Text Solution

    |

  13. The mean and variance of a binomial distribution B(n,p|) are 4 and 3.2...

    Text Solution

    |

  14. *' is an operation defined on Z set of all integers as a*b = a+b-2 for...

    Text Solution

    |

  15. *' is an operation defined on Z set of all integers as a*b = a+b-2 for...

    Text Solution

    |

  16. Show that sin^(-1) (12/13)+cos^(-1)(4/5)+tan^(-1)(63/16) = pi.

    Text Solution

    |

  17. If A = [[0,6,7],[-6,0,8],[7,-8,0]],B=[[0,1,1],[1,0,2],[1,2,0]],C=[[2],...

    Text Solution

    |

  18. If A = ([cos theta,sin theta],[-sin theta,cos theta]) show that A= ([c...

    Text Solution

    |

  19. show that |[1,x,x^2],[x^2,1,x],[x,x^2,1]| = (1-x^3)^2

    Text Solution

    |

  20. If (cos x)^y = (cos y)^x then show that (dy)/(dx) = (y tan x+log cos y...

    Text Solution

    |