lautstark
loud
With great volume; very loud. Describes noises, voices, or music.
Die Fans feierten den Sieg lautstark in der Innenstadt.
The fans celebrated the victory loudly in the city center.

loud / vociferous
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loud
With great volume; very loud. Describes noises, voices, or music.
Die Fans feierten den Sieg lautstark in der Innenstadt.
The fans celebrated the victory loudly in the city center.

'Lautstark' is a compound adjective made up of 'laut' (loud) and 'stark' (strong). So it literally means something like 'strongly loud' and intensifies the quality of being loud.
Die Kinder spielten lautstark im Garten.
The children played loudly in the garden.
'Lautstark' (loudly/vociferously) is very often used as an adverb to describe a verb. It then remains unchanged in the sentence and describes how an action is carried out.
Die Nachbarn haben bis spät in die Nacht lautstark Musik gehört.
The neighbors listened to music loudly until late into the night.
In the meaning of 'emphatically', 'lautstark' (vociferously) is often combined with verbs of demanding or criticizing. Typical phrases are 'lautstark protestieren' (to protest vociferously), 'lautstark fordern' (to demand vociferously), and 'lautstark kritisieren' (to criticize vociferously).
Die Bürgerinitiative forderte lautstark mehr Lärmschutzmaßnahmen.
The citizens' initiative vociferously demanded more noise-protection measures.
loud / according to
'laut' and 'lautstark' both describe something that is easy to hear. 'laut' is the normal, general word for high volume. 'lautstark' sounds stronger and emphasizes that something is very loud or impossible to miss. 'lautstark' is often used with voices, protest, criticism, or demands. For music, a conversation, or an everyday noise, 'laut' is usually enough; 'lautstark' fits better when the volume stands out or shows emphasis.

Die Fahrgäste beschwerten sich lautstark, weil der Zug wieder Verspätung hatte.
The passengers complained loudly because the train was delayed again.
Sie lacht so laut, dass man sie im ganzen Flur hört.
She laughs so loudly that you can hear her throughout the whole hallway.