高一数学~~~对数问题~~~~~~~~
\u5173\u4e8e\u9ad8\u4e00\u6570\u5b66\u5bf9\u6570\u95ee\u9898\u8bbe\u81f3\u5c11\u8981\u628ax\u5757\u8fd9\u6837\u7684\u73bb\u7483\u677f\u91cd\u53e0\u8d77\u6765(x\u2208Z)
\u7531\u9898\u610f:
(1-1/10)^x<1/3
\u22340.9^x<1/3
\u22350<0.9<1
\u2234log0.9(x)\u662f\u51cf\u51fd\u6570
\u4e24\u8fb9\u540c\u65f6\u53d6\u4ee50.9\u4e3a\u5e95\u7684\u5bf9\u6570
\u2234x>log0.9(1/3)
=lg(1/3)/lg0.9
=-lg3/(lg9+lg0.1)
=-lg3/(2lg3-1)
\u2235lg3\u22480.4771
\u2234x>10.5
\u2235x\u2208Z
\u2234x(min)=11
\u2234\u81f3\u5c11\u8981\u628a11\u5757\u8fd9\u6837\u7684\u73bb\u7483\u677f\u91cd\u53e0\u8d77\u6765\uff0c\u624d\u80fd\u4f7f\u901a\u8fc7\u5b83\u4eec\u7684\u5149\u7ebf\u5f3a\u5ea6\u5728\u613f\u5f3a\u5ea6\u76841/3\u4ee5\u4e0b
\uff081\uff09logaN^n=nlogaN
\u63a8\u5bfc\u516c\u5f0f\uff1a
\u7531\u5bf9\u6570\u52a0\u6cd5\u516c\u5f0f\uff1alogaM+logaN=logaMN\uff0c
n\u4e2alogaN\u76f8\u52a0\u5f97
logaN+ logaN+\u2026+logaN
=loga(N\u00d7N\u00d7\u2026\u00d7N) \uff08n\u4e2aN\u76f8\u4e58\uff09
=logaN^n\uff1b
\uff082\uff09\u5df2\u77e5a=lgx\uff0c\u5219a+3\u7b49\u4e8e\uff1f
a+3=lgx+3=lgx+lg1000=lg1000x\uff1b
\uff083\uff09\u82e52.5^x=1000\uff0c0.25^y=1000\uff0c\u5219(1/x)-(1/y)\u7b49\u4e8e\uff1f
\u22352.5^x=1000\uff0c
\u2234x=log1000\uff0c1/x=log2.5=(lg2.5)/3
(\u8868\u793a\u5e95\u6570\u662f2.5\uff0c\u5176\u4ed6\u7c7b\u4f3c)
\u22350.25^y=1000\uff0c
\u2234y=log1000\uff0c1/y=log0.25=(lg0.25)/3
(1/x)-(1/y)= (lg2.5)/3 - (lg0.25)/3=[(lg2.5) - (lg0.25)]/3=(lg10)/3=1/3\uff1b
\uff084\uff09\u8bbe\u51fd\u6570f\uff08x\uff09=logax\uff08a>0\u4e14a\u4e0d\u7b49\u4e8e0\uff09\uff0c\u82e5f\uff08x1x2\u2026x2010\uff09=8\uff0c
\u5219f\uff08x1²\uff09+f(x2²)+\u2026+f(x2010²)\u7684\u503c\u7b49\u4e8e\uff1f
\u2235f\uff08x1x2\u2026x2010\uff09=8\uff0c
\u2234log( x1x2\u2026x2010)=8\uff0c
\u5373logx1+logx2+\u2026+logx2010=8
f\uff08x1²\uff09+f(x2²)+\u2026+f(x2010²)
= logx1²+logx2²+\u2026+logx2010²
=2 logx1+2logx2+\u2026+2logx2010
=2 (logx1+logx2+\u2026+logx2010)
=2\u00d78
=16.
lg108
=lg(2²×3³)
=lg2²+lg3³
=2lg2+3lg3
=2a+3b
lg18/25
=lg72/100
=lg72-lg100
=lg(2³×3²)-lg10²
=lg2³+lg3²-2
=3lg2+2lg3-2
=3a+2b-2
2、
lg√2+lg√5
=lg(√2×√5)
=lg√10
=lg10的1/2次方
=1/2两个0
=1/2
log(3)45-log(3)5
=log3(45÷5)
=log3(9)
=log3(3²)
=2log3(3)
=2
1.
108=2*2*3*3*3
所以： lg108=lg2+lg2+lg3+lg3+lg3=2a+3b
lg18/25=lg72-lg100=lg(2*2*2*3*3)-2=3a+2b-2
2.
lg√2+lg√5=lg√10=1/2
log(3)45-log(3)5=log(3)[45/5]=log(3)9=2
绛旓細1銆乴g108 =lg(2²脳3³)=lg2²+lg3³=2lg2+3lg3 =2a+3b lg18/25 =lg72/100 =lg72-lg100 =lg(2³脳3²)-lg10²=lg2³+lg3²-2 =3lg2+2lg3-2 =3a+2b-2 2銆乴g鈭2+lg鈭5 =lg(鈭2脳鈭5)=lg鈭10 =lg10鐨1/2娆℃柟 =...
绛旓細1銆佸師寮=1/2*lg5²+lg2-1/2lg0.1-(lg9/lg2)*(lg2/lg3)=(lg5+lg2)-1/2*(-1)-(2lg3/lg2)*(lg2/lg3)=1+1/2-2 =-1/2 2銆佸師寮=(lg3/lg2)/(lg4/lg3)=(lg3/lg2)/(2lg2/lg3)=2 3銆佸彇瀵规暟 mlg2=nlg5=1 1/m=lg2,1/n=lg5 鎵浠ュ師寮=lg2+lg5=1 ...
绛旓細1.a^m*a^n=a^(m+n),m+n=log a MN,m+n=log a MN,log a MN=m+n 2.log a MN=log a M+log a N log a M/N=log a M-log a N log a M^n=nlog a M log c a/log c b=(lga/lgc )/(lgb/lgc)=lga/lgb=log a b 3.log a xy/z=log a x+log a y-log a ...
绛旓細鈶瀵规暟鐨勫畾涔夛細濡傛灉a(a>0,a鈮1)鐨刡娆″箓绛変簬N锛屽氨鏄痑^b=N锛岄偅涔堟暟b鍙仛浠涓哄簳N鐨勫鏁般傚洜涓篴>0锛屾墍浠ヤ笉璁篵鏄粈涔堝疄鏁帮紝閮芥湁a^b>0,杩欏氨鏄涓嶈b鏄粈涔堟暟锛孨姘歌繙鏄鏁帮紝鎵浠ヨ礋鏁板拰闆舵病鏈夊鏁 鈶℃帹瀵艰繃绋嬶細鑻ユ湁瀵规暟 鍒欐湁 (杩欎竴姝ワ紝璁綾^logca=x锛屽垯logca=logcx锛屽垯x=a)(涓よ竟鍚屾椂x...
绛旓細1瑙ｏ細f(x)=log2(x/8)*log1/2(4/x)=(log2(x)-3)(log2(x)-2)=[log2(x)-5/2]^2-1/4,鎵浠ュ綋鍦紙1/4锛8锛夋椂鐨勫煎煙涓篬-1/4锛,20锛2.鍥犱负A={xIy=1/鏍瑰彿锛坸-1)}锛孊={yIy=10-e^x},鎵浠={xIx锛1}锛孊={yIy锛10}锛屾墍浠 A鈭〣=锛1锛10)锛屾墍浠鈭圓鈭〣锛岄偅涔0...
绛旓細鍦ㄨ璁楂樹竴鏁板涓叧浜瀵规暟鍑芥暟log鐨闂鏃讹紝鎴戜滑棣栧厛鍒嗘瀽涓や釜鍑芥暟鐨勫畾涔夊煙銆傚嚱鏁癴(x)鐨勫畾涔夊煙涓簒 + 1 > 0锛屽嵆x > -1锛岃実(x)鐨勫畾涔夊煙涓4 - 2x > 0锛屽嵆x < 2銆傝鎵惧嚭f(x) - g(x)鐨勫畾涔夊煙锛屾垜浠渶瑕佹壘鍑鸿繖涓や釜鍑芥暟瀹氫箟鍩熺殑浜ら泦銆傝繖涓氦闆嗗氨鏄痜(x)鍜実(x)閮借兘鍙栧肩殑x鐨勮寖鍥达紝鍗...
绛旓細1銆佺敤鍒ゆ柇澧炲噺鐨勬渶鍩烘湰鐨勬柟娉曟潵鍋氥傝x1<x2涓旈兘涓哄畾涔夊煙鍐呯殑鏁帮紝鍒檉(x2)-f(x1)=log浠ヤ簩鍒嗕箣涓涓哄簳(x2+1)\(x1+1)鐨瀵规暟銆傜湡鏁版樉鐒跺ぇ浜1锛屾晠f(x2)-f(x1)<0锛屽嵆f(x)涓哄噺鍑芥暟銆2銆佸啀璁惧師鍑芥暟涓篺锛坸锛,棣栧厛瀹氫箟鍩熶负鍏ㄤ綋瀹炴暟锛屾墍浠ュ彧瑕佺畻涓涓媐锛-x锛夊氨濂姐傚湪鐪熸暟閮ㄥ垎闇瑕佺敤鍒板垎瀛...
绛旓細log14 56=lg56/lg14=(lg7+3lg2)/(lg2+lg7)=(3+lg7/lg2)/(1+lg7/lg2)=(3+ab)/(1+ab)3銆佽В娉1锛15+8+14=37,澶9浜,9-3-3=3,娌℃湁浜哄悓鏃跺弬鍔犱笁椤规瘮璧,鎵浠ュ悓鏃跺弬鍔犵敯寰勫拰鐞冪被姣旇禌鐨勬湁3浜.娌℃湁浜哄悓鏃跺弬鍔犱笁椤规瘮璧,15浜哄弬鍔犳父娉虫瘮璧,鏈6浜轰袱椤癸紝鎵浠15-6=9锛屽彧鍙傚姞娓告吵涓椤...
绛旓細lg X- lg y=lg 15-1 lg X- lg y=lg 15-lg10 锛堟敞锛歭ogaM-logaN=loga(M/N))lg(x/y)=log(15/10)x/y=3/2 (1)10^lg(3x+2y)=39 3x+2y=39 (2) (娉細a^logaM=M)鐢(1)(2),寰 x=9,y=6
绛旓細so easy!
