Marinada '22

[lang=hr] Znajući da voli matematiku, Dimitriju je djed iz daleke Rusije poslao staru zbirku zadataka. Čim je stigla, on uzbuđeno sjeda za radni stol i namjerno kreće s rješavanjem najstrašnijeg mu područja - logaritama. Pomozi Dimitriju da riješi zadatke i zavoli logaritme! \\ Koji racionalan broj $x$ zadovoljava sljedeću jednadžbu: $$\frac{1}{\log_2 x} + \frac{1}{\log_3 x} + \frac{1}{\log_4 x} = 1.$$ [/lang] \\ \\ [lang=en] Dimitri's grandfather knows how much his grandson loves mathematics, so he sent him an old workbook all the way from Russia. As soon as it arrived, Dimitri excitedly sits down at his desk and deliberately starts dealing with, for him, the scariest field in mathematics - logarithms. Help Dimitri solve the following exercises and get to like logarithms! \\ Find the rational number $x$ for which the following equation holds: $$\frac{1}{\log_2 x} + \frac{1}{\log_3 x} + \frac{1}{\log_4 x} = 1.$$ [/lang]