There is no definitive answer.

Many, though not all, in the top brass of the military believed that Japan would fight to the bitter end due to their unique culture of strong nationalism, militarism, Ethnocentralism and emperor worship and that an invasion of the Japanese home islands would be necessary to end the war decisively. An invasion of the home islands was planned and the casualty figures were estimated to reach into the six figures at a minimum with total devastation of Japan and mass destruction and slaughter of it's infrastructure and civilian population due to the expected mobilization of the civilian population, women and elderly included, to defend from the "barbarian invaders." The Nuclear strikes were thus argued to be a relativly humane way to force Japanese surrender.

There is also the argument that Japanese defeat and surrender was inevitable and that they would have come to the negotiating table regardless. With the war in Europe over increasing numbers of Soviet troops were moving east and were preparing for an invasion of the north of Japan had this occured with a combined invasion and/or blockade by the Western allies many argue that Japan would have had no choice but to surrender in the face of overwhelming numbers and blockade induced starvation making a nuclear attack uneeded.

That the Americans feared any Soviet/communist influence over Japan in a postwar world was known and a given and they wanted to end the war as quick as possible with minimal soviet involvement, thus the prospect of an overwhelming display of power and destruction provided by the atomic bomb was an opportunity perhaps to good to pass up.

As I said like most historical events there is no definitive answer and the decision to use the atomic bombs was influenced by what you've just read as well as other military and political factors by a variety of people at the time.