The phrase "logical outgrowth" means that something is a natural result or consequence of a particular situation or idea. It is when a conclusion or development follows logically from what has come before. Full definition
The conclusion must be the logical outgrowth, the consummation of what went before, not the starting place. (religion-online.org)
The inevitability of sin is not a logical outgrowth of man's situation in nature and spirit; but temptation to sin lies in this situation. (religion-online.org)
In a church that has a strong commitment to covenant theology, that practice would seem to be the logical outgrowth of the theological premises, but the measure is being strongly opposed by those who feel that it would represent a serious lowering of the solemnity of the sacramental occasion. (religion-online.org)