eq = 2*z*Log[a*v2^2/b2] + (v1 - 2*v2) - z*Log[a*v1^2/b1] >= 0;

sol = First@Solve[b21 == b2/b1, b1];

eq2 = eq /. sol

(*   v1 - 2 v2 - z Log[(a b21 v1^2)/b2] + 2 z Log[(a v2^2)/b2] >= 0   *)

Simplify[Reduce[eq2, b21, Reals]] /. b21 -> b2/b1

eq = 2*z*Log[a*v2^2/b2] + (v1 - 2*v2) - z*Log[a*v1^2/b1] >= 0;

sol = First@Solve[b21 == b2/b1, b1];

eq2 = eq /. sol

(*   v1 - 2 v2 - z Log[(a b21 v1^2)/b2] + 2 z Log[(a v2^2)/b2] >= 0   *)

sred = Simplify[Reduce[eq2, b21, Reals]] /. b21 -> b2/b1 

TraditionalForm[
sred //. Or -> 
Composition[(Column[#, Right, Background -> {{White, LightGray}}, 
   Frame -> All] &), List]]