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)
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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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