ð 察æ°èšç®æ©
å€xãšåº(base)ãå ¥åããã ãã§ãä»»æã®åºã§ã®å¯Ÿæ°(log_base(x))ãèšç®ã§ããããŒã«ã§ããåºã10ã®åžžçšå¯Ÿæ°ããèªç¶å¯Ÿæ°(ln)ã®å€ãåæã«ç¢ºèªã§ããŸããæ°åŠã®å®¿é¡ããææ°é¢æ°çãªå€å(pHå€ã»ãã·ãã«ã»å°éã®ãã°ããã¥ãŒããªã©)ã®çè§£ã«åœ¹ç«ã¡ãŸãã
äœ¿ãæ¹
- å€x(æ£ã®æ°)ãå ¥åããŸãã
- åº(æ£ã®æ°ã1以å€)ãå ¥åããŸãã
- æå®ããåºã§ã®å¯Ÿæ°ãšèªç¶å¯Ÿæ°(ln)ãèªåçã«èšç®ãããŸãã
èšç®ã®ä»çµã¿
察æ°ïŒlogïŒã¯ããããæ°ãäœä¹ããã°ç®çã®æ°ã«ãªãããã衚ãå€ã§ããlogâx ïŒ y ã¯ãaÊž ïŒ x ãšåãæå³ã§ãaããåºïŒãŠãïŒããšåŒã³ãŸãã ãã®ããŒã«ã¯ãåºã®å€æå ¬åŒã䜿ã£ãŠãä»»æã®åºã®å¯Ÿæ°ãèšç®ããŸãã logâx ïŒ ln x ÷ ln a ln ã¯ããã€ãã¢æ° eïŒçŽ2.71828ïŒãåºãšããèªç¶å¯Ÿæ°ã§ããããããŠãå ¥åããæ°ã®èªç¶å¯Ÿæ°ã衚瀺ããŸããåºã¯1以å€ã®æ£ã®æ°ãçæ°ïŒxïŒã¯æ£ã®æ°ã§ããå¿ èŠããããŸãã
èšç®äŸ
logââ100 ïŒ 2ïŒ10² ïŒ 100ïŒ logâ8 ïŒ 3ïŒ2³ ïŒ 8ïŒ ln 100 â 4.605 logâ1,000,000 â 19.93 ãªã®ã§ã100äžã2鲿°ã§è¡šãã«ã¯20ãããå¿ èŠã§ãã é³ã®å€§ããã®ãã·ãã«ãå°éã®ãã°ããã¥ãŒããé žæ§åºŠã®pHã¯ã察æ°ã䜿ã£ã尺床ã§ãã
䜿çšäžã®æ³šæ
- çæ°ã0以äžãåºã1ã0以äžã®å Žåã¯ã察æ°ã¯å®çŸ©ãããªãããèšç®ã§ããŸããã
- åžžçšå¯Ÿæ°ïŒåº10ïŒã®å€ã®æŽæ°éšåããããã®æ°ã®æ¡æ°ãããããŸããlogââx ã®æŽæ°éšå ïŒ 1 ããx ã®æŽæ°éšåã®æ¡æ°ã§ãã
- èšç®ã¯å°æ°ïŒæµ®åå°æ°ç¹æ°ïŒã§è¡ããããããããããªèª€å·®ãåºãããšããããŸãã
ãããã質å
åžžçšå¯Ÿæ°(logââ)ãèšç®ããã«ã¯?
åºã®æ¬ã«10ãå ¥åããŠãã ããããããããã©ã«ãã®èšå®ã§ãã
èªç¶å¯Ÿæ°(ln)ãšã¯äœã§ãã?
ãã€ãã¢æ°e(çŽ2.71828)ãåºãšãã察æ°ã®ããšã§ããçµæã«ã¯åžžã«èªåçã«è¡šç€ºãããŸãã
xãåºã«0以äžã®å€ãå ¥åãããšã©ããªããŸãã?
察æ°ã¯æ£ã®æ°ã«å¯ŸããŠã®ã¿å®çŸ©ãããããã0以äžã®å€ãå ¥åãããšçµæã衚瀺ãããŸããããŸãåºã«1ã¯äœ¿çšã§ããŸããã