“And he brought them out [of the dungeon] and said, Men, what is it necessary for me to do that I may be saved? And they answered, Believe in the Lord Jesus Christ [[a]give yourself up to Him, [b] take yourself out of your own keeping and entrust yourself into His keeping] and you will be saved, [and this applies both to] you and your household as well.” Acts 16:30-31
http://www.biblegateway.com/passage/?search=Acts%2016:30-31&version=AMP
Keep reading that passage.
You know what happens next, don’t you?
Here. I’ll post if for you.
31 They replied, Believe in the Lord Jesus, and you will be savedyou and your household. 32 Then they spoke the word of the Lord to him and to all the others in his house. 33 At that hour of the night the jailer took them and washed their wounds; then immediately he and all his household were baptized. 34 The jailer brought them into his house and set a meal before them; he was filled with joy because he had come to believe in Godhe and his whole household.
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When Paul and Silas “spoke the word of the Lord” to him, that included the command to be baptized. And he and his household were!
Which is precisely the definition of obedience. If you're "in Christ's keeping," you're no longer your own master. You have a master, because you have been "bought at a price," and you owe him your obedience. That's why Paul writes in Romans that he came to bring "the obedience of faith to all the nations" (Rom 1:5)
It's very dangerous to take single Scripture verses out of context and string them together to try to justify a theological point.
A classic case is Ps 14:3 ("there is none who does good, no, not one"), which wmfights "Gospel" quotes almost immediately. Looking at it in context (which is certainly how Paul understood it), you find that it's hyperbolic. Ps 14 contrasts the wicked, of whom "none [do] good" with "my people" (verse 4) and "the generation of the righteous" (verse 5), so 14:3 is clearly not talking about all people, everywhere, without exception, for all time.