ln(a-b)还可以往下化吗？ 为什麼ln(a+b)约等於(a-b)/b？
ln(a+b)\u5982\u4f55\u62c6\u5206Ln(a + b) = Lna * Ln[1 + (b/a)] = Lnb * Ln[1 + (a/b)]
\u81ea\u7136\u5bf9\u6570\u4ee5\u5e38\u6570e\u4e3a\u5e95\u6570\u7684\u5bf9\u6570\u3002\u8bb0\u4f5clnN(N>0)\u3002\u5728\u7269\u7406\u5b66\uff0c\u751f\u7269\u5b66\u7b49\u81ea\u7136\u79d1\u5b66\u4e2d\u6709\u91cd\u8981\u7684\u610f\u4e49\u3002\u4e00\u822c\u8868\u793a\u65b9\u6cd5\u4e3alnx\u3002\u6570\u5b66\u4e2d\u4e5f\u5e38\u89c1\u4ee5logx\u8868\u793a\u81ea\u7136\u5bf9\u6570\u3002\u82e5\u4e3a\u4e86\u907f\u514d\u4e0e\u57fa\u4e3a10\u7684\u5e38\u7528\u5bf9\u6570lgx\u6df7\u6dc6\uff0c\u53ef\u7528\u201c\u5168\u5199\u201d\u33d2ex\u3002
\u5e38\u6570e\u7684\u542b\u4e49\u662f\u5355\u4f4d\u65f6\u95f4\u5185\uff0c\u6301\u7eed\u7684\u7ffb\u500d\u589e\u957f\u6240\u80fd\u8fbe\u5230\u7684\u6781\u9650\u503c\u3002
\u81ea\u7136\u5bf9\u6570\u7684\u5e95e\u662f\u7531\u4e00\u4e2a\u91cd\u8981\u6781\u9650\u7ed9\u51fa\u7684\u3002\u6211\u4eec\u5b9a\u4e49\uff1a\u5f53n\u8d8b\u4e8e\u65e0\u7a77\u5927\u65f6\uff0c .
e\u662f\u4e00\u4e2a\u65e0\u9650\u4e0d\u5faa\u73af\u5c0f\u6570\uff0c\u5176\u503c\u7ea6\u7b49\u4e8e2.718281828459\u2026\uff0c\u5b83\u662f\u4e00\u4e2a\u8d85\u8d8a\u6570\u3002
\u6269\u5c55\u8d44\u6599\uff1a
\u5f53\u81ea\u7136\u5bf9\u6570 \u4e2d\u771f\u6570\u4e3a\u8fde\u7eed\u81ea\u53d8\u91cf\u65f6\uff0c\u79f0\u4e3a\u5bf9\u6570\u51fd\u6570\uff0c\u8bb0\u4f5c \uff08x\u4e3a\u81ea\u53d8\u91cf\uff0cy\u4e3a\u56e0\u53d8\u91cf\uff09\u3002
\u95ee\u9898\uff1a\u6c42\u590d\u6570 \u7684\u5bf9\u6570\uff0c\u89c4\u5b9a \u4e3a \u7684\u5e45\u89d2\u4e3b\u503c\u3002
\u89e3\u7b54\uff1a
\u8bbe\u6709\u4e00\u590d\u6570 \uff0c\u5176\u901a\u8fc7\u6307\u6570\u51fd\u6570 \u5c06 \u6620\u5c04\u4e3a \u3002
\u2234 \u7531\u590d\u6570\u76f8\u7b49\u7684\u5b9a\u4e49\uff0c\u5f97\u5230\uff1a
\u6240\u4ee5 \uff0c\u5373 \u8bb0 \u4e3a\u5bf9\u6570\u51fd\u6570\uff0c\u53ef\u4ee5\u770b\u5230\u5728\u590d\u6570\u4e2d\u5bf9\u6570\u51fd\u6570\u662f\u591a\u503c\u51fd\u6570\uff08\u5373\u4e00\u4e2a\u81ea\u53d8\u91cf\u5bf9\u5e94\u591a\u4e2a\u56e0\u53d8\u91cf\uff09\uff0c\u5e76\u4e14\u6709\u65e0\u6570\u4e2a\u5206\u652f\u3002\u7279\u522b\u5730\uff0c\u5f53k=0\u65f6\uff0c\u79f0 \u4e3a\u5bf9\u6570\u51fd\u6570\u7684\u4e3b\u503c\u652f\uff0c\u6b64\u65f6\u7528\u8bb0\u53f7 \u6765\u8868\u793a\u3002
\u5373w\u7684\u5b9e\u90e8\u4e3az\u7684\u6a21\u53d6\u81ea\u7136\u5bf9\u6570\uff0c\u865a\u90e8\u4e3az\u7684\u5e45\u89d2\u4e3b\u503c\u3002\u8fd9\u5c31\u662f\u5f53\u771f\u6570\u4e3a\u590d\u6570\u65f6\u7684\u5bf9\u6570\u8fd0\u7b97\u516c\u5f0f\u3002\u6ce8\u610f\uff0c\u56e0\u4e3a\u5b9e\u90e8\u9700\u8981\u5bf9z\u7684\u6a21\u53d6\u81ea\u7136\u5bf9\u6570\uff0c\u56e0\u6b64r\u22600\u3002\u6211\u4eec\u77e5\u9053\u5728\u590d\u5e73\u9762\u4e0a\u53ea\u67090\u8fd9\u4e2a\u590d\u6570\u7684\u6a21\u4e3a0\uff0c\u5176\u4ed6\u4efb\u4f55\u590d\u6570\u7684\u6a21\u90fd\u5927\u4e8e0\uff0c\u6240\u4ee5\u5728\u590d\u6570\u57df\u4e2d\uff0c\u9664\u4e86z=0\u4ee5\u5916\u6240\u6709\u7684\u590d\u6570\u90fd\u53ef\u4ee5\u6c42\u5bf9\u6570\u3002
\u53c2\u8003\u8d44\u6599\uff1a\u767e\u5ea6\u767e\u79d1\u2014\u2014\u81ea\u7136\u5bf9\u6570
\u8bbea>b>0,\u8bc1\u660e\uff1a(a-b)/a<lna/b<(a-b)/b
\u8bc1\uff1a\u8bbef(x)=lnx
\u5219\uff1af'(x)=1/x;
\u6839\u636e\u62c9\u683c\u6717\u65e5\u4e2d\u503c\u5b9a\u7406f(a)-f(b)=f'(u)(a-b)(0<b<u<a),
\u6240\u4ee5f'(u)=[f(a)-f(b)]/(a-b),
\u5373\uff1a1/u=[lna-lnb]/(a-b),
\u6240\u4ee5lna/b=(a-b)/u,
\u53c8\u56e0\u4e3a(0<b<u<a)
, \u6240\u4ee5(a-b)/a<lna/b<(a-b)/b
\u53ea\u662f\u8bf4 ln(a/b)\u4ecb\u4e8e (a-b)/a \u548c (a-b)/b \u4e4b\u95f4,
\u4f46\u662f\u5e76\u6ca1\u6709\u8bf4 ln(a/b)\u7ea6\u7b49\u4e8e(a-b)/b, \u4e0d\u8fc7\u5f53 a, b \u76f8\u5dee\u4e0d\u5927\u65f6, \u53ef\u4ee5\u7ea6\u7b49\u4e8e.
如ln(a-b)=lna(1-b/a)=lna+ln(1-b/a)=lnb+ln(a/b-1)等等
No,
不可以了
绛旓細Ln(a + b) = Lna * Ln[1 + (b/a)] = Lnb * Ln[1 + (a/b)]鑷劧瀵规暟浠ュ父鏁癳涓哄簳鏁扮殑瀵规暟銆傝浣渓nN(N>0)銆傚湪鐗╃悊瀛︼紝鐢熺墿瀛︾瓑鑷劧绉戝涓湁閲嶈鐨勬剰涔夈備竴鑸〃绀烘柟娉曚负lnx銆傛暟瀛︿腑涔熷父瑙佷互logx琛ㄧず鑷劧瀵规暟銆傝嫢涓轰簡閬垮厤涓庡熀涓10鐨勫父鐢ㄥ鏁發gx娣锋穯锛屽彲鐢ㄢ滃叏鍐欌濄彃ex銆傚父鏁癳鐨勫惈涔夋槸...
绛旓細瀵圭殑銆ln(a/b)=lna-lnb锛宭n(ab)=lna+lnb銆傚鏁扮殑杩愮畻娉曞垯锛1銆乴og(a) (M路N锛=log(a) M+log(a) N 2銆乴og(a) (M梅N)=log(a) M-log(a) N 3銆乴og(a) M^n=nlog(a) M 4銆乴og(a)b*log(b)a=1 5銆乴og(a) b=log (c) b梅log (c) a ...
绛旓細Ln锛坅+b锛= Lna * Ln[1 + (b/a)]= Lnb * Ln[1 + (a/b)]鑷劧瀵规暟浠ュ父鏁癳涓哄簳鏁扮殑瀵规暟銆傝浣渓nN(N>0)銆傚湪鐗╃悊瀛︼紝鐢熺墿瀛︾瓑鑷劧绉戝涓湁閲嶈鐨勬剰涔夈備竴鑸〃绀烘柟娉曚负lnx銆傛暟瀛︿腑涔熷父瑙佷互logx琛ㄧず鑷劧瀵规暟銆傝嫢涓轰簡閬垮厤涓庡熀涓10鐨勫父鐢ㄥ鏁發gx娣锋穯锛屽彲鐢ㄢ滃叏鍐欌濄彃ex銆
绛旓細Ln锛坅+b锛= Lna * Ln[1 + (b/a)]= Lnb * Ln[1 + (a/b)]鑷劧瀵规暟浠ュ父鏁癳涓哄簳鏁扮殑瀵规暟銆傝浣渓nN(N>0)銆傚湪鐗╃悊瀛︼紝鐢熺墿瀛︾瓑鑷劧绉戝涓湁閲嶈鐨勬剰涔夈備竴鑸〃绀烘柟娉曚负lnx銆傛暟瀛︿腑涔熷父瑙佷互logx琛ㄧず鑷劧瀵规暟銆傝嫢涓轰簡閬垮厤涓庡熀涓10鐨勫父鐢ㄥ鏁發gx娣锋穯锛屽彲鐢ㄢ滃叏鍐欌濄彃ex銆傚姞娉曠畝浠 鍔犳硶锛堥氬父...
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