{"id":10511,"date":"2025-07-15T13:34:50","date_gmt":"2025-07-15T13:34:50","guid":{"rendered":"https:\/\/functiontranslator.com\/log\/"},"modified":"2021-02-26T05:20:29","modified_gmt":"2021-02-26T05:20:29","slug":"log","status":"publish","type":"post","link":"https:\/\/functiontranslator.com\/pl\/log\/","title":{"rendered":"LOG"},"content":{"rendered":"<h2>Wprowadzenie do funkcji w Excelu i Google Tabelach<\/h2>\n<p>Funkcja LOG s\u0142u\u017cy do obliczania logarytmu liczby. U\u017cytkownik mo\u017ce okre\u015bli\u0107 podstaw\u0119 logarytmu, a je\u015bli jej nie poda, domy\u015blnie funkcja zwr\u00f3ci logarytm naturalny. Ta funkcja jest szczeg\u00f3lnie przydatna w analizie danych w dziedzinach takich jak nauka, ekonomia i finanse, gdzie cz\u0119sto analizuje si\u0119 wzrost i zmiany procentowe.<\/p>\n<h2>Syntaksis funkcji<\/h2>\n<p>W programie Excel sk\u0142adnia funkcji LOG wygl\u0105da nast\u0119puj\u0105co:<\/p>\n<pre><code>=LOG(liczba, [podstawa])<\/code><\/pre>\n<p>Argumenty tej funkcji to:<\/p>\n<ul>\n<li><strong>liczba<\/strong> \u2013 liczba, dla kt\u00f3rej obliczany jest logarytm. Musi by\u0107 ona dodatnia.<\/li>\n<li><strong>podstawa<\/strong> \u2013 podstawa systemu logarytmicznego. Je\u015bli nie zostanie okre\u015blona, domy\u015blnie stosowana jest podstawa e (logarytm naturalny).<\/li>\n<\/ul>\n<p>W Google Tabelach sk\u0142adnia funkcji LOG jest identyczna:<\/p>\n<pre><code>=LOG(liczba, [podstawa])<\/code><\/pre>\n<p>Argumenty funkcji s\u0105 takie same jak w Excelu.<\/p>\n<h2>Przyk\u0142adowe zastosowania<\/h2>\n<p>Ni\u017cej znajduj\u0105 si\u0119 praktyczne przyk\u0142ady wykorzystania funkcji LOG.<\/p>\n<h2>1. Obliczenie stopnia kwasowo\u015bci roztworu<\/h2>\n<p>W chemii pH roztworu wyra\u017ca si\u0119 jako logarytm dziesi\u0119tny odwrotno\u015bci st\u0119\u017cenia jon\u00f3w H+. Aby u\u017cy\u0107 funkcji LOG do obliczenia pH, nale\u017cy zna\u0107 st\u0119\u017cenie jon\u00f3w H+.<\/p>\n<p>Na przyk\u0142ad, przy st\u0119\u017ceniu H+ r\u00f3wnym 0.0001 mol\/L, pH roztworu mo\u017cna obliczy\u0107 w nast\u0119puj\u0105cy spos\u00f3b:<\/p>\n<pre><code>=LOG(0.0001, 10)<\/code><\/pre>\n<p>Wynik 4 oznacza, \u017ce pH roztworu wynosi 4.<\/p>\n<h2>2. Obliczanie z\u0142o\u017conego oprocentowania<\/h2>\n<p>Logarytmy mo\u017cna r\u00f3wnie\u017c u\u017cy\u0107 do okre\u015blenia czasu potrzebnego do podwojenia warto\u015bci inwestycji przy danym oprocentowaniu rocznym. Wz\u00f3r na obliczenie tego czasu to:<\/p>\n<pre><code>T = LOG(2) \/ LOG(1 + r)<\/code><\/pre>\n<p>Gdzie <strong>r<\/strong> to roczna stopa procentowa wyra\u017cona w formie u\u0142amka dziesi\u0119tnego.<\/p>\n<p>Przyk\u0142adowo, przy stopie procentowej 5%, czas potrzebny do podwojenia inwestycji wyniesie:<\/p>\n<pre><code>=LOG(2) \/ LOG(1 + 0.05)<\/code><\/pre>\n<p>Przy u\u017cyciu logarytmu naturalnego wynik to oko\u0142o 14.21 lat.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Zwraca logarytm danej liczby przy zadanej podstawie<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[423],"tags":[],"class_list":["post-10511","post","type-post","status-publish","format-standard","hentry","category-matematyczne-i-trygonometryczne"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v23.8 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Funkcja LOG w Excelu \u2013 jak dzia\u0142a, przyk\u0142ady u\u017cycia i sk\u0142adnia<\/title>\n<meta name=\"description\" content=\"Opis funkcji LOG w Excelu. 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