If `x=(log)_(2a)a , y=(log)_(3a)2a ,z=(log)_(4a)3a` ,prove that `1+x y z=2y z`

If ("log"x)/(y - z) = ("log" y)/(z - x) = ("log" z)/(x - y) , then prove that xyz = 1.

If ("log"_(e)x)/(b - c) = ("log"_(e) y)/(c - a) = ("log"_(e) z)/(a - b) , show that xyz = 1

If y= 2^((1)/(log_(x)4)) then prove that x=y^(2) .

If y=a^(1/(1-(log)_a x)) and z=a^(1/(1-(log)_a y)) ,then prove that x=a^(1/(1-(log)_a z))

The x , y , z are positive real numbers such that (log)_(2x)z=3,(log)_(5y)z=6,a n d(log)_(x y)z=2/3, then the value of (1/(2z)) is ............

If x y^2=4a n d(log)_3((log)_2x)+(log)_(1/3)((log)_(1/2)y)=1 ,then x equals (a) 4 (b) 8 (c) 16 (d) 64

Solve x^((log)_y x)=2a n dy^((log)_x y)=16

If ("log"_(e)x)/(b - c) = ("log"_(e) y)/(c - a) = ("log"_(e) z)/(a - b) , show that x^(a)y^(b)z^(c ) = 1

If (log)_2x+(log)_x2=(10)/3=(log)_2y+(log)_y2a n dx=y ,t h ex+y= 2 (b) 65/8 (c) 37/6 (d) none of these

If (log_2x)/4=(log_2y)/6=(log_2z)/(3k) and x^3 y^2 z=1 , then k is equal to