(v) `1/log_x (xyz)+1/log_y (xyz)+1/log_z (xyz)=1`

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)]|

Let L denots value of cos^(2)(alpha - beta) if sin2alpha + sin2beta = (1)/(2), cos2alpha + cos2beta = (sqrt(3))/(2) and M denotes value of (1)/(log_(xy)xyz) + (1)/(log_(yz)xyz) + (1)/(log_(zx)xyz) then 16L^(2) + M^(2) is

The numbers 1/3, 1/3 log _(x) y, 1/3 log _(y) z, 1/7 log _(x) x are in H.P. If y= x ^® and z =x ^(s ), then 4 (r +s)=

The numbers 1/3, 1/3 log _(x) y, 1/3 log _(y) z, 1/7 log _(x) x are in H.P. If y= x ^r and z =x ^(s ), then 4 (r +s)=

Solve: log_axlog_a(xyz)=48 ; log_aylog_a(xyz)=12 ; log_azlog_a(xyz)=84

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

Solve the system of equations: (log)_a x(log)_a(x y z)=48(log)_a y log_a(x y z)=12 ,\ a >0,\ a!=1(log)_a z log_a(x y z)=84\

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……

If xy^(2) = 4 and log_(3) (log_(2) x) + log_(1//3) (log_(1//2) y)=1 , then x equals

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