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

Solve the system of equations : log_(a)(x)log_(a)(xyz)=48log_(a)(y)log_(a)(xyz)=12log_(a)(z)log_(a)(xyz)=84,quad a>0,a!=1

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\

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\

Solve the system of equations: (log)_(a)x(log)_(a)(xyz)=48(log)_(a)y log_(a)(xyz)=12,backslash a>0,backslash a!=1(log)_(a)z log_(a)(xyz)=84

(1)/(log_(xy)(xyz))+(1)/(log_(yz)(xyz))+(1)/(log_(zx)(xyz))=

det[[log_(x)xyz,log_(x)y,log_(x)zlog_(y)xyz,1,log_(y)zlog_(z)xyz,log_(z)y,1]]=0

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

If x=log_(b)a,y=log_(c)b,z=log_(a)c then xyz=

Let x , y and z are real numbers satisfying the system of equations log_(2)(xyz-3+log_(5)x)=5 log_(3)(xyz-3+log_(5)y)=4 log_(4)(xyz-3+log_(5)z)=4 then the value of |log_(5)x|+|log_(5)y|+|log_(5)z| is