Answer:
The United States dropping the atomic bombs on Japan was not justifiable, since history has proven many times over that solving long term issues through violence will only most likely result in one of two solutions. The anger against each side lasts for at least as long as the issue was around. Or the other, it will be 'solved' for a short time, and even then will it only come back to more disagreements among the people, causing more violence, or better, just verbal debates and disagreements, although that rarely happens in large issues among nations.
When the US dropped the bombs, they were expecting a quick surrender of Japan, although it would have been better with less violence, talking it out, or even a smaller-range bomb, that wouldn't kill so much of the population and destroy so much land. The United States dropped the bomb for a personal benefit of a lower amount of American lives lost, contradicting the idea amongst most people to preserve all human life, and prevent death from occurring as much as possible. The action was personally considered an 'allegation', not legally, among many people; many others believe that it was necessary and justifiable. It would be difficult to gainsay others opinions on this matter, although you can certainly attempt to proselytize.
Partial Rebuttal for a more beneficial answer:
After dropping the first bomb, Japan had still not surrendered, enticing the United States to repeat the action. To have two bombs dropped on your own country after being warned would most likely make you want to surrender or obey the warring nation. In the end, it turned out to be a gain for the United States, and a great loss for Japan, basically the overall idea of the people of the United States.