Home
Class 12
MATHS
Evaluate the determinant =|(log)3 512...

Evaluate the determinant `=|(log)_3 512(log)_4 3(log)_3 8(log)_4 9|` .

Text Solution

AI Generated Solution

To evaluate the determinant \[ D = \begin{vmatrix} \log_3 512 & \log_4 3 \\ \log_3 8 & \log_4 9 \end{vmatrix} \] ...
Promotional Banner

Topper's Solved these Questions

  • DERIVATIVES AS A RATE MEASURER

    RD SHARMA|Exercise Solved Examples And Exercises|149 Videos

  • DIFFERENTIABILITY

    RD SHARMA|Exercise Solved Examples And Exercises|136 Videos

Similar Questions

Explore conceptually related problems

Q.Evaluate the determinant Delta=|(log_(3)512log_(4)3),log_(3)8log_(4)9)|

|(log)_3 512(log)_4 3(log)_3 8(log)_4 9|xx|(log)_2 3(log)_8 3(log)_3 4(log)_3 4|= (a) 7 (b) 10 (c) 13 (d) 17

Which of the following when simplified reduces to unity? (log)_(3/2)(log)_4(log)_(sqrt(3))81 (log)_2 6+(log)_2sqrt(2/3) -1/6(log)_(sqrt(3/2))((64)/(27)) (d) (log)_(7/2)(1+2-3-:6)

Determine the value of log_4 {log_sqrt2(log_3 81)}

Comprehension 2 In comparison of two numbers, logarithm of smaller number is smaller, if base of the logarithm is greater than one. Logarithm of smaller number is larger, if base of logarithm is in between zero and one. For example log_2 4 is smaller than (log)_2 8 a n d(log)_(1/2)4 is larger than (log)_(1/2)8. Identify the correct order: (log)_2 6 (log)_3 8> log_3 6>(log)_4 6 (log)_3 8>(log)_2 6> log_3 6>(log)_4 6 (log)_2 8<(log)_4 6

The value of 3^((log)_4 5)+4^((log)_5 3)-5^((log)_4 3)-3^((log)_5 4) is- a.0 b. 1 c.2 d. none of these

Which of the following are correct? a.(log)_3 19.(log)_(1//7)3.(log)_4 1/7>2 b. (log)_5(1//23) lies between -2&-1 c. If m=4^((log)_4 7)a n d n=(1/9)^(-(log)_3 7)t h e n n=m^4 d. (log)_(sqrt(5))sin(pi/5)dot(log)_(sqrt(sin"pi"/5))5 simplifies to an irrational number

Find the value of the expressions (log2)^3+log8.log(5)+(log5)^3 .

The value of |[log_3 1024, log_3 3],[log_3 8, log_3 9]| xx|[log_2 3, log_4 3],[log_3 4, log_3 4]|

RD SHARMA-DETERMINANTS-Solved Examples And Exercises
  1. If |x-2-3 3x2x|=3 , find the values of xdot

    Text Solution

    |

  2. Let |[3,y],[x,1]|=|[3,2],[4,1]| Find possible values of x and y if x,y...

    Text Solution

    |

  3. Evaluate the determinant =|(log)3 512(log)4 3(log)3 8(log)4 9| .

    Text Solution

    |

  4. Find the minors of cofactors of elements of the matrix A=[a(i j)]=[[1,...

    Text Solution

    |

  5. Let A=|1sintheta1-sintheta1sintheta-1-sintheta1|, where 0lt=thetalt=2p...

    Text Solution

    |

  6. If [ ] denotes the greatest integer less than or equal to the real nu...

    Text Solution

    |

  7. Prove that the determinant |(x,sin theta,cos theta),(-sin theta,-x,1),...

    Text Solution

    |

  8. Write the minors and cofactors of each element of the first column ...

    Text Solution

    |

  9. Write the minors and cofactors of each element of the first column ...

    Text Solution

    |

  10. Evaluate the following determinants: |x-7x5x+1| (ii) |costheta-sin...

    Text Solution

    |

  11. Evaluate the following determinants: |x-7x5x+1| (ii) |costheta-sin...

    Text Solution

    |

  12. Evaluate: |2 3 7 13 17 5 15 20 12|^2 .

    Text Solution

    |

  13. Show that |sin10o-cos10osin80ocos80o|=1

    Text Solution

    |

  14. Evaluate |2 3-5 7 1-2-3 4 1| by two methods.

    Text Solution

    |

  15. Evaluate: =|0sinalpha-cosalpha-sinalpha0sinbetacosalpha-sinbeta0|

    Text Solution

    |

  16. Evaluate: =|cosalphacosbetacosalphasinbeta-sinalpha-sinbetacosbeta0sin...

    Text Solution

    |

  17. If A=[2 5 2 1] and B=[4-3 2 5] , verify that |A B|=|A||B| .

    Text Solution

    |

  18. If A=[[1 ,0 ,1],[0 ,1, 2],[ 0, 0, 4]] , then show that |3A|" "=" "27|...

    Text Solution

    |

  19. Find the values of x , if |2 4 5 1|=|2x4 6x| (ii)|2 3 4 5|=|x3 2x5| (...

    Text Solution

    |

  20. Find the values of x , if |3x7 2 4|=10 (ii) |x+1x-1x-3x+2|=|4-1 1 3| ...

    Text Solution

    |