Logan's body was discovered in July 2021 in the River Ogmore near his home in Sarn, Bridgend county.
Craig Mulligan, 14, was sentenced to 15 years in prison after being convicted alongside Logan's mother and stepfather.
After reviewing his sentence, the Attorney General's Office decided not to appeal it to the Court of Appeal.
Logan's father, John Cole, must serve at least 29 years in prison, while Logan's mother, Angharad Williamson, must serve at least 28 years.
Why can murderer Craig Mulligan now be labelled as having "serious concerns" with children's services? "The solicitor general was horrified by this case and wishes to express his condolences to the victim's father," an Attorney General's Office spokesman said.
"The solicitor general has concluded that this case cannot be properly referred to the Court of Appeal after careful consideration.
Logan Mwangi had previously been described as a "smiling, cheerful little boy" at the trial "A referral to the Court of Appeal under the Unduly Lenient Sentence scheme can only be made if a sentence is not just lenient but unduly so that the sentencing judge made a gross error or imposed a sentence that was outside the range of sentences reasonably available in the circumstances of the offence.
"The test was not passed in this case because the threshold was too high."
Mulligan, Cole, and Williamson killed the Tondu Primary School student before dumping him in the river in nearby Pandy Park, jurors at his trial were told.
Logan was discovered partially submerged, wearing dinosaur pyjama bottoms and a Spider-Man top.
For Logan's murder, John Cole and Angharad Williamson are also serving lengthy prison sentences. Logan was treated like a prisoner in the days leading up to his death, despite previously being described as a "smiling, cheerful little boy," and died at home after a "brutal and sustained" attack.
He sustained 56 "catastrophic" injuries, including extensive bruising to the back of his head and tears in his liver and intestine.
Mulligan pushed Logan down the stairs, breaking his arm, because he had a "desire for violence."
"I love to punch kids in the head, it's orgasmic," he once sang to a support worker.
Logan Mwangi, five, was described as a "really sweet, happy-go-lucky child" by a neighbour. Mrs Justice Jefford told the trio in court that they were "all responsible for Logan's death and all the anguish that has flowed from it."
"Because he was killed in his own home, we don't know what happened to him," she explained.
Mulligan could not be identified publicly during the trial due to reporting restrictions imposed by his age.
This was lifted after he was found guilty and sentenced.
Mrs Justice Jefford stated in her decision on the anonymity order that if Mulligan was not named, "there is a significant gap in any understanding of this case."