Ok, interesting. I was disappointed to see that the answer was "you can't really expand it". My initial thought was to break it up so I could view the whole thing, so here I share with you how I do just that (not that it's anything fancy nor is it near efficient, but it gets the job done in a pinch):

if (sb.length() > 4000) {
    Log.v(TAG, "sb.length = " + sb.length());
    int chunkCount = sb.length() / 4000;     // integer division
    for (int i = 0; i <= chunkCount; i++) {
        int max = 4000 * (i + 1);
        if (max >= sb.length()) {
            Log.v(TAG, "chunk " + i + " of " + chunkCount + ":" + sb.substring(4000 * i));
        } else {
            Log.v(TAG, "chunk " + i + " of " + chunkCount + ":" + sb.substring(4000 * i, max));
        }
    }
} else {
    Log.v(TAG, sb.toString());
}

Edited to show the last string!