If x, y, z are positive real numbers such that none of them is unity and log_xy, log_zx, log_yz are in G.P. x³, y³, z³ are in A.P. and xyz = 216, then the value of x + y + 2z is equal to

Log x y, log z y, log y z - in GPLet log x y =A Log z x=B Log y z = CSo B/A=C/BWe get log x^3=log z^3So 3 log x=3 log zSo log x=log z X=ZGiven x^3,y^3,z^3 in APSO 2Y^3=X^3+Z^3=2X^3SO X=YWE GET X=Y=ZSO X=Y=Z=6 AS XYZ=216SO X+Y+2Z= 6+6+12=24