If `log_ex- log_ey =a, log_ey- log_ez= b & log_ez- log_ex =c`, then find the value of `(x/y)^(b-c).(y/z)^(c-a).(z/x)^(a-b) = ?`

If log_(theta)x-log_(theta)y= a, log_(theta)y-log_(theta)z=b and log_(theta)z- log_(theta)x=c , then find the value of (x/y)^(b-c) x(y/z)^(c-a)x(z/x)^(a-b)

If log_(theta)x-log_(theta)y= a, log_(theta)y-log_(theta)z=b and log_(theta)z- log_(theta)x=c , then find the value of (x/y)^(b-c) x(y/z)^(c-a)x(z/x)^(a-b)

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

Let log_(c)ab = x, log_(a)bc = y and log_(b) ca = z . Find the value of (xyz - x - y - z) .

Let log_(c)ab=x,log_(a)bc=y and log_(b)ca=z Find the value of (xyz-x-y-z)

If (log x)/(b-c) = (log y)/(c-a) = (log z)/(a-b) , then prove that x^(b+c).y^(c+a).z^(a+b) = 1

(1+log_(c)a)log_(a)x*log_(b)c=log_(b)x log_(a)x