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Ecuatii si inecuatii logaritmice

... pot incadra intr-un anumit tip.Astfel,pot aparea ecuatii cu logaritmi scrisi in diferite baze,ecuatii in care apar expresii continand necunoscute si la exponenti si la logaritmi etc.5Sa se rezolve ecuatialog2xlog3x1.Deducem,aplicand formula de schimbare a bazei, EMBED Equation.3 sau lgx EMBED Equation.3 Deci x10 EMBED Equation.3 .6Sa se rezolve ecuatialog3xlogx32.Deoarece logx3 EMBED Equation.3 ,rezulta log3x EMBED Equation.3 2.Notand log3xy,obtinem y EMBED Equation.3 ,adica y2-2y10deci y1,adica log3x1.Prin urmare,x3.7Sa se rezolve ecuatiaxlgx21000.Punem conditia de existenta a expresiilorx0.Logaritmand,obtinem o ecuatie echivalenta lgxlgx2lg1000 care devine lgx2lgx3.Notand lgxy,avem y22y-30 si deci y1-3,y21.Din lgx-3,obtinem x10-3,x0,001,iar din lgx1,rezulta x10. irxhjvx .nIIII56CJHaJmHsH56CJHaJmHsHaj56CJEHUaJajY1ACJUVaJ
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