{"id":5676,"date":"2025-07-15T13:34:45","date_gmt":"2025-07-15T13:34:45","guid":{"rendered":"https:\/\/functiontranslator.com\/ln\/"},"modified":"2021-02-26T09:58:54","modified_gmt":"2021-02-26T09:58:54","slug":"ln","status":"publish","type":"post","link":"https:\/\/functiontranslator.com\/cs\/ln\/","title":{"rendered":"LN"},"content":{"rendered":"

Funkce LN v Microsoft Excel a Google Sheets slou\u017e\u00ed k v\u00fdpo\u010dtu p\u0159irozen\u00e9ho logaritmu \u010d\u00edsla, co\u017e je logaritmus o z\u00e1kladu konstanty e (p\u0159ibli\u017en\u011b rovno 2.71828). P\u0159irozen\u00fd logaritmus m\u00e1 kl\u00ed\u010dovou roli v mnoha oblastech, jako jsou anal\u00fdza dat, ekonomie, biologie a dal\u0161\u00ed v\u011bdn\u00ed discipl\u00edny. Tato funkce pom\u00e1h\u00e1 p\u0159ev\u00e1d\u011bt exponenci\u00e1ln\u00ed r\u016fst na line\u00e1rn\u00ed, co\u017e usnad\u0148uje jeho anal\u00fdzu a interpretaci.<\/p>\n

Popis a syntaxe funkce<\/h2>\n

Syntaxe funkce LN je v aplikac\u00edch Microsoft Excel a Google Sheets stejn\u00e1:<\/p>\n

=LN(\u010d\u00edslo)<\/code><\/pre>\n
    \n
  • \u010d\u00edslo<\/strong> \u2013 Hodnota, pro kterou chceme vypo\u010d\u00edtat p\u0159irozen\u00fd logaritmus. Toto \u010d\u00edslo mus\u00ed b\u00fdt kladn\u00e9, jeliko\u017e logaritmus ze z\u00e1porn\u00fdch hodnot nen\u00ed v re\u00e1ln\u00fdch \u010d\u00edslech definov\u00e1n.<\/li>\n<\/ul>\n
    Pokud zadan\u00e9 \u010d\u00edslo nen\u00ed kladn\u00e9, funkce vr\u00e1t\u00ed chybovou hl\u00e1\u0161ku.<\/p>\n
    Praktick\u00e9 pou\u017eit\u00ed<\/h2>\n
    P\u0159\u00edklad 1: V\u00fdpo\u010det \u010dasu zdvojn\u00e1soben\u00ed investice<\/h2>\n
    P\u0159edstavte si investora, kter\u00fd pot\u0159ebuje zjistit, jak dlouho trv\u00e1, ne\u017e se jeho investice zdvojn\u00e1sob\u00ed za p\u0159edpokladu konstantn\u00ed ro\u010dn\u00ed \u00farokov\u00e9 sazby. K tomuto \u00fa\u010delu lze pou\u017e\u00edt pravidlo 70, co\u017e je osv\u011bd\u010den\u00e1 metoda v ekonomii.<\/p>\n
    =LN(2) \/ LN(1 + \u00farokov\u00e1 m\u00edra)<\/code><\/pre>\n
    P\u0159i p\u0159edpokladu ro\u010dn\u00ed \u00farokov\u00e9 m\u00edry 5 % (0.05 v desetinn\u00e9m tvaru) bychom pou\u017eili n\u00e1sleduj\u00edc\u00ed v\u00fdpo\u010det:<\/p>\n
    =LN(2) \/ LN(1 + 0.05)<\/code><\/pre>\n
    To by v\u00fdsledn\u011b odhadlo dobu zdvojn\u00e1soben\u00ed investice na p\u0159ibli\u017en\u011b 13,51 let, co\u017e investorovi umo\u017en\u00ed pl\u00e1novat s lep\u0161\u00ed p\u0159edstavou o v\u00fdvoji jeho investic.<\/p>\n
    P\u0159\u00edklad 2: Anal\u00fdza r\u016fstu bakteri\u00ed<\/h2>\n
    V biologii a ekologii je \u010dasto pot\u0159eba analyzovat popula\u010dn\u00ed r\u016fst, kter\u00fd m\u00e1 exponenci\u00e1ln\u00ed charakter. P\u0159irozen\u00fd logaritmus umo\u017e\u0148uje tato data transformovat na line\u00e1rn\u00ed form\u00e1t, co\u017e zjednodu\u0161uje dal\u0161\u00ed anal\u00fdzu. Za p\u0159edpokladu, \u017ee po\u010det bakteri\u00ed P po t hodin\u00e1ch je d\u00e1n vzorcem P = P0<\/sub> * ekt<\/sup>, kde k je konstanta r\u016fstu, m\u016f\u017ee b\u00fdt funkce LN vyu\u017eita k ur\u010den\u00ed hodnoty k:<\/p>\n
    k = (LN(P) - LN(P0)) \/ t<\/code><\/pre>\n
    Nap\u0159\u00edklad, za\u010d\u00edn\u00e1me-li s 50 bakteriemi a po 3 hodin\u00e1ch jich m\u00e1me 400, v\u00fdpo\u010det konstanty r\u016fstu k by byl:<\/p>\n
    k = (LN(400) - LN(50)) \/ 3<\/code><\/pre>\n
    Tento v\u00fdpo\u010det poskytne hodnotu k, kterou lze d\u00e1le vyu\u017e\u00edt k anal\u00fdze a predikc\u00edm r\u016fstu populac\u00ed bakteri\u00ed nebo ke srovn\u00e1n\u00ed r\u016fstov\u00fdch rychlost\u00ed mezi r\u016fzn\u00fdmi kmeny.<\/p>\n
    Tak je funkce LN nezbytnou sou\u010d\u00e1st\u00ed n\u00e1stroj\u016f pro pr\u00e1ci s daty v Excelu a Google Sheets, a poskytuje kritick\u00e9 informace pro r\u016fzn\u00e9 v\u011bdeck\u00e9 a aplikovan\u00e9 discipl\u00edny.<\/p>\n","protected":false},"excerpt":{"rendered":"
    Vr\u00e1t\u00ed p\u0159irozen\u00fd logaritmus \u010d\u00edsla<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[282],"tags":[],"class_list":["post-5676","post","type-post","status-publish","format-standard","hentry","category-matematicke-a-trigonometricke"],"acf":[],"yoast_head":"\nFunkce LN v Excelu: jak funguje, primjeri kori\u0161tenja formule<\/title>\n<meta name=\"description\" content=\"Opis funkcije LN u Excelu i Google tablicama. 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