>>338
log3{(3^x+3^y)/2}≧log3{3^((x+y)/2)}≧(x+y)/2 　等号は x=y

x+y = (x+loga) + (y+logb) - (loga+logb)　（log の底は 3）
≦2log3{(3^(x+loga)+3^(y+logb)/2)} - log3(ab)
= 2log3{a*3^x+b*3^y} -log3(ab)
≦log3{4/(ab)}

log3(ab) = 2-{log3(a)}^2+log3(a) = -{log3(a) -1/2}^2 + 5/4 ≦5/4
M = log3{4} - log3{ab} ≧ 2log3{2} - 5/4