ln(a-b)=lna-lnb吗 ln(a+b)等于lna+lnb吗？
ln(a/b)=lna-lnb ln(ab)=lna+lnb\u662f\u4e0d\u662f\uff1f\u5bf9\u7684\u3002
ln(a/b)=lna-lnb\uff0cln(ab)=lna+lnb\u3002
\u5bf9\u6570\u7684\u8fd0\u7b97\u6cd5\u5219\uff1a
1\u3001log(a) (M\u00b7N\uff09=log(a) M+log(a) N
2\u3001log(a) (M\u00f7N)=log(a) M-log(a) N
3\u3001log(a) M^n=nlog(a) M
4\u3001log(a)b*log(b)a=1
5\u3001log(a) b=log (c) b\u00f7log (c) a
\u6269\u5c55\u8d44\u6599
\u81ea\u7136\u5bf9\u6570\u7684\u6765\u6e90\uff1a
\u57281614\u5e74\u5f00\u59cb\u6709\u5bf9\u6570\u6982\u5ff5\uff0c\u7ea6\u7ff0\u00b7\u7eb3\u76ae\u5c14\u4ee5\u53caJost B\u00fcrgi\uff08\u82f1\u8bed\uff1aJost B\u00fcrgi\uff09\u57286\u5e74\u540e\uff0c\u5206\u522b\u53d1\u8868\u4e86\u72ec\u7acb\u7f16\u5236\u7684\u5bf9\u6570\u8868\uff0c\u5f53\u65f6\u901a\u8fc7\u5bf9\u63a5\u8fd11\u7684\u5e95\u6570\u7684\u5927\u91cf\u4e58\u5e42\u8fd0\u7b97\uff0c\u6765\u627e\u5230\u6307\u5b9a\u8303\u56f4\u548c\u7cbe\u5ea6\u7684\u5bf9\u6570\u548c\u6240\u5bf9\u5e94\u7684\u771f\u6570\uff0c\u5f53\u65f6\u8fd8\u6ca1\u51fa\u73b0\u6709\u7406\u6570\u5e42\u7684\u6982\u5ff5\u3002
1742\u5e74William Jones\uff08\u82f1\u8bed\uff1aWilliam Jones (mathematician)\uff09\u624d\u53d1\u8868\u4e86\u5e42\u6307\u6570\u6982\u5ff5\u3002\u6309\u540e\u6765\u4eba\u7684\u89c2\u70b9\uff0cJost B\u00fcrgi\u7684\u5e95\u65701.0001\u76f8\u5f53\u63a5\u8fd1\u81ea\u7136\u5bf9\u6570\u7684\u5e95\u6570e\uff0c\u800c\u7ea6\u7ff0\u00b7\u7eb3\u76ae\u5c14\u7684\u5e95\u65700.99999999\u76f8\u5f53\u63a5\u8fd11/e\u3002
\u5b9e\u9645\u4e0a\u4e0d\u9700\u8981\u505a\u5f00\u9ad8\u6b21\u65b9\u8fd9\u79cd\u8270\u96be\u8fd0\u7b97\uff0c\u7ea6\u7ff0\u00b7\u7eb3\u76ae\u5c14\u7528\u4e8620\u5e74\u65f6\u95f4\u8fdb\u884c\u76f8\u5f53\u4e8e\u6570\u767e\u4e07\u6b21\u4e58\u6cd5\u7684\u8ba1\u7b97\uff0cHenry Briggs\uff08\u82f1\u8bed\uff1aHenry Briggs (mathematician)\uff09\u5efa\u8bae\u7eb3\u76ae\u5c14\u6539\u752810\u4e3a\u5e95\u6570\u672a\u679c\uff0c\u4ed6\u7528\u81ea\u5df1\u7684\u65b9\u6cd5\u4e8e1624\u5e74\u90e8\u4efd\u5b8c\u6210\u4e86\u5e38\u7528\u5bf9\u6570\u8868\u7684\u7f16\u5236\u3002
\u4e00\u822c\u60c5\u51b5\u4e0bln(a+b)\u4e0elna+lnb\u4e0d\u76f8\u7b49\uff0c\u6b63\u786e\u7684\u5173\u7cfb\u662f\uff1alna+lnb=ln(ab)\u3002
\u4f46\u5f53a+b=ab\u65f6\uff0c\u8fd9\u4e24\u4e2a\u5f0f\u5b50\u5c31\u662f\u76f8\u7b49\u7684\uff0c\u4f8b\u5982a=b=2.
\u5176\u4e2dlnx\u662f\u4e00\u79cd\u7279\u6b8a\u7684\u5bf9\u6570\u2014\u2014\u81ea\u7136\u5bf9\u6570\uff0c\u4e5f\u5c31\u662f\u4ee5e\u4e3a\u5e95\u6570\u7684\u5bf9\u6570\uff0c\u5176\u4e2de\u22482.7.
\u5173\u4e8e\u5bf9\u6570\u7684\u8ba1\u7b97\u516c\u5f0f\u5e38\u7528\u7684\u5982\u4e0b\uff1a
1\u3001
2\u3001
3\u3001
4\u3001
5\u3001
6\u3001
这两个式子是不等的
绛旓細閿欙紒搴旇鏄細ln锛坅/b锛=lna-lnb
绛旓細In (a-b)灏辨槸In (a-b)ln(a/b)=lna-lnb ln(ab)=lna+lnb
绛旓細ln(a-b)=lna/lnb(a>0,b>0,b鈮1)
绛旓細娌℃湁涓嶪n(a-b)鐩稿叧鐨勫叕寮 涓嬮潰鏄笌瀵规暟鏈夊叧鐨勫叕寮忥紝甯屾湜瀵逛綘鏈夊府鍔 鏈涢噰绾宠阿璋 绁濆涔犺繘姝
绛旓細鏈夌殑锛lna-lnb=ln(a/b)鏈夎繖涓叕寮
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绛旓細鍦ㄦ暟瀛︿腑锛lna-lnb鏄寚浠ヨ嚜鐒跺鏁帮紙浠涓哄簳锛変负鍩虹鐨勫鏁拌繍绠楋紝琛ㄧずlna-lnb鐨勭粨鏋溿傚叾涓紝ln琛ㄧず鑷劧瀵规暟鍑芥暟锛宎鍜宐鏄湡鏁帮紙姝ｅ疄鏁帮級锛宎 > 0锛宐 > 0锛屽苟涓攁鈮燽銆傞氳繃璁＄畻ln(a/b)锛屽彲浠ュ緱鍒發na-lnb鐨勭粨鏋溿傞渶瑕佹敞鎰忕殑鏄紝瀵规暟杩愮畻鐨勭粨鏋滃彲鑳芥槸瀹炴暟鎴栧鏁帮紝鍏蜂綋鍙栧喅浜庤姹傚鏁扮殑鏁板笺傚鏁版槸...
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绛旓細涓嶅锛ln(a/b) = lna - lnb銆備笖浠呭綋a>0涓攂>0鏃讹紝ln(a/b)=lna-lnb锛宭n(ab)=lna+lnb姝ｇ‘銆傚叾瀹炰綘鍙互鐢╳indows鑷甫鐨勮绠楀櫒璇曚竴涓嬶細ln2=0.69314718055994530941723212145818 ln5=1.6094379124341003746007593332262 ln2+ln5=2.3025850929940456840179914546842 ln10=2.3025850929940456840179914546844 a鍙仛...
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