  Let L be an ample line bundle on a log variety (V, D) having only log
terminal singularities.The Kodaira energy of such a triple (V, D, L) is defined
as follows: \kappa\epsilon=-Inf{t\in Q | K(V,D)+tL is big}. Here K(V,D)=K_V+D
is the log canonical bundle of (V,D) and "big" means \kappa=dim V. We first
show that the rationality of \kappa\epsilon, when it is negative, follows from
log Flip theorems (thus it is proved for dim V\le 3 at present). Second we
consider the case in which D=0, dim V=3 and V has only terminal singularities.
Let S be the set of all the possible values of Kodaira energies of such
polarized log threefolds. We prove that S has no negative limit point. This
result is closely related to the boundedness of Fano 3-folds.
