`log_(2)log_(3)log_(4)log_(5)^((5)^((4)^((3)^((2)))))=?`

log_(5)4*log_(2)5

3log_(2)5+log_(2)10-log_(2)625

(log_(2)3)(log_(1/3)5)(log_(4)6)<1

If log_(x){log_(4)(log_(x)(5x^(2)+4x^(3)))}=0, then

(log_(5)4)(log_(4)3)(log_(3)2)(log_(2)1) =

The value of log_(3)[log_(2){log_(4)(log_(5)625^(4))}] is ______.

If log_(2)(log_(4)(x))) = 0, log_(3)(log_(4)(log_(2)(y))) = 0 and log_(4)(log_(2)(log_(3)(z))) = 0 then the sum of x,y and z is-

If x=(2)^((log_(2)3log_(3)4log_(4)5)......log_(19)20),y=5^(log_(2)3)-3^(log_(2)5),z=log_(sqrt(256))sqrt(log_(sqrt(2))4) then value of (x+y).z is

let E=log_(2)(log_(2)3)+log_(2)(log_(3)4)+log_(2)(log_(4)5)+log_(2)(log_(5)6)+log_(2)(log_(6)7)+log_(2)(log_(7)8 then 8^(E) is

The expression: (((x^(2)+3x+2)/(x+2))+3x-(x(x^(3)+1))/((x+1)(x^(2)+1))-log_(2)8)/((x-1)(log_(2)3)(log_(3)4)(log_(4)5)(log_(5)2)) reduces to