Having the knowledge of God leads to life because the implication is that if you know God’s character then it gives us the basis for faith in him and also transforms our character so that we can be like him thus proving him to be our Father and us his sons/daughters.
We can only be imitators of God if we know his character. As was in Hosea’s day, the world today shows by their deeds that it does not have the knowledge of God. All we have to do is turn on the news or go outside.