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...
绛旓細锛4锛夎嫢寮忎腑骞傛寚鏁板垯鏈変互涓嬬殑姝f暟鐨勭畻鏈牴鐨勫鏁拌繍绠楁硶鍒:涓涓鏁扮殑绠楁湳鏍圭殑瀵规暟锛岀瓑浜庤寮鏂规暟鐨勫鏁伴櫎浠ユ牴鎸囨暟锛屽嵆锛氳嚜鐒跺鏁颁互甯告暟e涓哄簳鏁扮殑瀵规暟锛岃浣渓nN(N>0)銆傛暟瀛︿腑涔熷父瑙佷互logx琛ㄧず鑷劧瀵规暟锛屾墍浠nx鐨勮绠楁柟寮忎篃鍙互鍒╃敤濡備笂鍏紡銆2銆乴n2-ln1鍒╃敤濡備笂鍏紡锛2锛夊緱锛歭n2-ln1=ln锛2/1锛...
绛旓細鍦ㄦ暟瀛︿腑锛宭g鍜宭n鏄袱涓父鐢ㄧ殑瀵规暟鍑芥暟锛屽垎鍒〃绀轰互10涓哄簳鐨勫鏁板拰浠涓哄簳鐨勮嚜鐒跺鏁般傚畠浠箣闂村彲浠ラ氳繃鎹㈠簳鍏紡杩涜杞崲銆傛崲搴曞叕寮忓涓嬶細濡傛灉a>0涓攁鈮1锛宐>0涓攂鈮1锛屽垯鏈夛細ln(a^b) = b * ln(a)lg(a^b) = b * lg(a)鍏朵腑锛宎鍜宐鍒嗗埆鏄簳鏁帮紝ln琛ㄧず鑷劧瀵规暟锛宭g琛ㄧず浠10涓哄簳鐨勫鏁...
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绛旓細lna+lnb=2ln(a-b)ln(ab)=2ln(a-b)=ln(a-b)^2 鈭碼b=(a-b)^2 鍗砤b=a^2-2ab+b^2 鈭碼^2-3ab+b^2=0 鈭碼=(3卤鈭5)b/2 鑰宎-b>0锛屾墍浠>b>0 鈭碼/b>1 鈭碼/b=(3+鈭5)/2 鈭磍og2(a/b)=log2[(3+鈭5)/2]...
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