Home
Class 12
MATHS
for x,x,z gt 0 Prove that |{:(1,,log(x)y...

for `x,x,z gt 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`

A

0

B

1

C

`-1`

D

none

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    BITSAT GUIDE|Exercise BITSAT ARCHIVES |13 Videos
  • DEFINITE INTEGRALS AND ITS APPLICATIONS

    BITSAT GUIDE|Exercise BITSAT Archives |25 Videos
  • DIFFERENTIAL COEFFICIENTS

    BITSAT GUIDE|Exercise BITSAT Archives|17 Videos

Similar Questions

Explore conceptually related problems

det[[log_(x)xyz,log_(x)y,log_(x)zlog_(y)xyz,1,log_(y)zlog_(z)xyz,log_(z)y,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 ):}| =

For positive numbers x,y,s the numberical value of the determinant |{:(1,log_(x)y,log_(x)z),(log_(y)x,3,log_(y)z),(log_(z)x,log_(z)y,5):}| is

For positive numbers x, y and z, the numerical value of the determinant |{:(1,"log"_(x)y, "log"_(x)z),("log"_(y)x, 1, "log"_(y)z),("log"_(z)x, "log"_(z)y, 1):}| is……

For positive numbers x,y and z, the numerical value of the determinant det[[log_(x)y,log_(x)zlog_(y)x,1,log_(y)zlog_(z)x,log_(z)y,1]]

If x gt 0 , y gt 0 , z gt 0 , the least value of x^(log_(e)y-log_(e)z)+y^(log_(e)z-log_(e)x)+Z^(log_(e)x-log_(e)y) is

log_(x)x xx log_(y)y xx log_(z)z = ______

log_(x rarr n)-log_(a)y=a,log_(a)y-log_(a)z=b,log_(a)z-log_(a)x=c

The value of the determinant ,log_(a)((x)/(y)),log_(a)((y)/(z)),log_(a)((z)/(x))log_(b)((y)/(z)),log_(b)((z)/(x)),log_(b)((x)/(y))log_(c)((z)/(x)),log_(c)((x)/(y)),log_(c)((y)/(z))]|

For positive numbers x ,\ y\ a n d\ z the numerical value of the determinant |1(log)_x y(log)_x z(log)_y x1(log)_y z(log)_z x(log)_z y1| is- a. 0 b. logx y z c. "log"(x+y+z) d. logx\ logy\ logz