高中数学log求详解
log \u662f\u4ec0\u4e48 \uff0c\u600e\u4e48\u6837\u4f7f\u7528\u7684\uff0c\uff1f\u9ad8\u4e00\u6570\u5b66log\u662f\u5bf9\u6570\u7684\u8868\u8fbe\u5f0f
\u5982 a²=b
\u5219loga\uff08b\uff09=2
\u5c31\u662f\u6307\u4ee5a\u4e3a\u5e95\uff0cb\u7684\u5bf9\u6570\u5c31\u662f2
\u4ee510\u4e3a\u5e95\u7684\u5bf9\u6570\u8868\u793a\u65b9\u6cd5\u4e3alg\u3002
\u5bf9\u6570\u5e38\u7528\u516c\u5f0f\uff1a
\u5bf9\u6570\u7684\u6027\u8d28\u53ca\u63a8\u5bfc\u3000\u3000\u5b9a\u4e49\uff1a \u82e5a^n=b(a>0\u4e14a\u22601) \u5219n=log(a)(b)
\u3000\u3000\u57fa\u672c\u6027\u8d28\uff1a
\u3000\u30001\u3001a^(log(a)(b))=b
\u3000\u30002\u3001log(a)(MN)=log(a)(M)+log(a)(N);
\u3000\u30003\u3001log(a)(M\u00f7N)=log(a)(M)-log(a)(N);
\u3000\u30004\u3001log(a)(M^n)=nlog(a)(M)
\u3000\u30005\u3001log(a^n)M=1/nlog(a)(M)
\u3000\u3000\u63a8\u5bfc\uff1a
\u3000\u30001\u3001\u56e0\u4e3an=log(a)(b)\uff0c\u4ee3\u5165\u5219a^n=b\uff0c\u5373a^(log(a)(b))=b\u3002
\u3000\u30002\u3001MN=M\u00d7N
\u3000\u3000\u7531\u57fa\u672c\u6027\u8d281(\u6362\u6389M\u548cN)
\u3000\u3000a^[log(a)(MN)] = a^[log(a)(M)]\u00d7a^[log(a)(N)]
\u3000\u3000\u7531\u6307\u6570\u7684\u6027\u8d28
\u3000\u3000a^[log(a)(MN)] = a^{[log(a)(M)] + [log(a)(N)]}
\u3000\u3000\u53c8\u56e0\u4e3a\u6307\u6570\u51fd\u6570\u662f\u5355\u8c03\u51fd\u6570\uff0c\u6240\u4ee5
\u3000\u3000log(a)(MN) = log(a)(M) + log(a)(N)
\u3000\u30003\u3001\u4e0e\uff082\uff09\u7c7b\u4f3c\u5904\u7406 MN=M\u00f7N
\u3000\u3000\u7531\u57fa\u672c\u6027\u8d281(\u6362\u6389M\u548cN)
\u3000\u3000a^[log(a)(M\u00f7N)] = a^[log(a)(M)]\u00f7a^[log(a)(N)]
\u3000\u3000\u7531\u6307\u6570\u7684\u6027\u8d28
\u3000\u3000a^[log(a)(M\u00f7N)] = a^{[log(a)(M)] - [log(a)(N)]}
\u3000\u3000\u53c8\u56e0\u4e3a\u6307\u6570\u51fd\u6570\u662f\u5355\u8c03\u51fd\u6570\uff0c\u6240\u4ee5
\u3000\u3000log(a)(M\u00f7N) = log(a)(M) - log(a)(N)
\u3000\u30004\u3001\u4e0e\uff082\uff09\u7c7b\u4f3c\u5904\u7406
\u3000\u3000M^n=M^n \u7531\u57fa\u672c\u6027\u8d281(\u6362\u6389M) a^[log(a)(M^n)] = {a^[log(a)(M)]}^n
\u3000\u3000\u7531\u6307\u6570\u7684\u6027\u8d28
\u3000\u3000a^[log(a)(M^n)] = a^{[log(a)(M)]*n}
\u3000\u3000\u53c8\u56e0\u4e3a\u6307\u6570\u51fd\u6570\u662f\u5355\u8c03\u51fd\u6570\uff0c\u6240\u4ee5
\u3000\u3000log(a)(M^n)=nlog(a)(M)
\u3000\u3000\u57fa\u672c\u6027\u8d284\u63a8\u5e7f
\u3000\u3000log(a^n)(b^m)=m/n*[log(a)(b)]
\u3000\u3000\u63a8\u5bfc\u5982\u4e0b\uff1a \u7531\u6362\u5e95\u516c\u5f0f\uff08\u6362\u5e95\u516c\u5f0f\u89c1\u4e0b\u9762\uff09[lnx\u662flog(e)(x)\uff0ce\u79f0\u4f5c\u81ea\u7136\u5bf9\u6570\u7684\u5e95] log(a^n)(b^m)=ln(b^m)\u00f7ln(a^n)
\u3000\u3000\u6362\u5e95\u516c\u5f0f\u7684\u63a8\u5bfc\uff1a \u8bbee^x=b^m,e^y=a^n \u5219log(a^n)(b^m)=log(e^y)(e^x)=x/y x=ln(b^m),y=ln(a^n) \u5f97\uff1alog(a^n)(b^m)=ln(b^m)\u00f7ln(a^n)
\u3000\u3000\u7531\u57fa\u672c\u6027\u8d284\u53ef\u5f97 log(a^n)(b^m) = [m\u00d7ln(b)]\u00f7[n\u00d7ln(a)] = (m\u00f7n)\u00d7{[ln(b)]\u00f7[ln(a)]}
\u3000\u3000\u518d\u7531\u6362\u5e95\u516c\u5f0f log(a^n)(b^m)=m\u00f7n\u00d7[log(a)(b)]
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绛旓細鎴戠殑 楂樹腑鏁板log姹傝瑙 鎴戞潵绛 2涓洖绛 #鐑# 浣犺寰楀悓灞呬細鏇村鏄撹鎰熸儏鍙樻贰鍚?killatw 楂樼矇绛斾富 2015-02-10 路 鍏虫敞鎴戜笉浼氳浣犲け鏈 鐭ラ亾澶ф湁鍙负绛斾富 鍥炵瓟閲:1.7涓 閲囩撼鐜:89% 甯姪鐨勪汉:2980涓 鎴戜篃鍘荤瓟棰樿闂釜浜洪〉 鍏虫敞 灞曞紑鍏ㄩ儴 鏈洖绛旂敱鎻愰棶鑰呮帹鑽 宸茶禐杩 宸茶俯杩< 浣犲杩欎釜...
绛旓細1銆傝В锛歛=1/log₂3+1/log₅3=log₃2+log₃5=log₃10锛宭og₃9<log₃10<log₃27锛屽嵆2<a<3.鏁呴塂銆2銆傚嚱鏁皔=log‹a›[(2x+1)/(x-1)]锛宎>0锛屼笖a鈮1锛屽凡鐭ュ嚱鏁板浘鍍忎笂鏈変竴鐐筆锛屽垯P鐨勫潗鏍囦负锛欰(1锛0)锛汢(-2锛0)...
绛旓細瑙: 鍥犱负 log浠2涓哄簳3鐨勫鏁=ln3/ln2 鑰宭n3/ln2>1/ln2 ln3/ln2-1>1/ln2-1 |ln3/ln2-1 |> |1/ln2-1 | 鎵浠 ,2^|ln3/ln2-1 |>2^ |1/ln2-1 | 鍗 b>a log浠3涓哄簳1/2鐨勫鏁=-ln2/ln3 |-ln2/ln3-1|>|ln3/ln2-1| 鎵浠 ,2^|-ln2/ln3-1|>2^...
绛旓細=loga(2-(-x)) (-x鈭圼0,1]=loga(2+x)鎵浠 f(x)= loga(2+x) x鈭圼-1,0]loga(2-x) x鈭圼0,1]2銆佸綋x鈭圼-1,0]鏃讹紝f(x)= loga(2+x) 閫掑 褰搙鈭圼0,1]鏃 F(x)=loga(2-x) 閫掑噺 x鈭圼-1,1]f(x)max=f(0)=loga(2-0)=1/2 a=4 褰搙鈭圼0,1]鏃 f(x)=lo...
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绛旓細搴旇娌℃湁绠楅敊
绛旓細鍒嗗瓙鍒嗘瘝鍚屾椂涔樷垰2-1 鍒嗗瓙鐢卞钩鏂瑰樊鍏紡鍙煡涓1锛屽垎瀛愬紡鈭2-1锛屽氨鍑鸿繖涓瓟妗堜簡
绛旓細=log2[f(a1)+log2f(a2)+..log2f(a10)=log2(2^a1)+log2*(2^a2)+...log2(2^a10)=a1+a2+...a10;绛夊樊鏁板垪{an}鐨勫叕宸负2;a2-2=a1 a4-2=a3;..a10-2=a9;a2+a4+a6+a8+a10-10=a1+a3+a5+a7+a9;a1+a2+a3+a...a10=2(a2+a4+a6+a8+a10)-10;f(a2+a4+a6+a8+a10)=...
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