[[[1,log_x y, log_z x],[log_y x, 1 , log_y z],[log_z x, log_z y, 1]]`=0

For positive numbers x, y and z, the numerical value of the determinant |[1,log_xy,log_xz],[log_yx,1,log_yz],[log_zx,log_zy,1]| is

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

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\ 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

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)]|

Solve for x, y , z . log_2 x + log_4 y + log_4 z =2 log_3 y + log_9 z + log_9 x =2 log_4 z + log_16 x + log_16 y =2

Prove that the value of each the following determinants is zero: |[logx,logy,logz],[ log2x ,log2y ,log2z ],[log3x, log3y ,log3z]|

. If 1, log_y x, log_z y, -15 log_x z are in AP, then

If "log"_(y) x = "log"_(z)y = "log"_(x)z , then

x^((log_x)log_a ylog_y z) is equal to