一些高一的数学的对数题！
\u9ad8\u4e00\u7684\u6570\u5b66\u5bf9\u6570\u9898\u89e3\uff1a\uff081\uff09y=lg\uff08x²+mx+1\uff09\u7684\u5b9a\u4e49\u57df\u4e3aR
\u5373x²+mx+1\uff1e0\u5728x\u2208R\u6052\u6210\u7acb
\u2234\u25b3=m²-4\uff1c0
m\u2208\uff08-2,2\uff09
(2)\u2235x²+mx+1=\uff08x+m/2)²+1-\uff08m²/4\uff09
y=lg\uff08x²+mx+1\uff09\u7684\u503c\u57df\u4e3aR
\uff08\u4e5f\u5c31\u662fx²+mx+1\u53ef\u4ee5\u53d6\u52300\u5230\u6b63\u65e0\u7a77\u5185\u6240\u6709\u503c\uff0c\u5373\u6700\u5c0f\u503c\u22640\uff09
\u22341-\uff08m²/4\uff09\u22640
\u2234m\u2208\uff08\uff0d\u221e,2]\u222a[2,\uff0b\u221e\uff09
2^\uff081+log(2)5\uff09\uff1f\u5e94\u8be5\u662f2^\uff081+0.5log(2)5\uff09\u5427\uff01
1.a^m*a^n=a^(m+n),m+n=log a MN,m+n=log a MN,log a MN=m+n2.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 z
log a （x^2乘上y的平方根/z的立方根)
=2log a x+(1/2)log a y-(1/3)log a z
4.①log 2 (4^7乘上2^5)=log 2 4^7+log 2 2^5
=7log 2 4 +5log 2 2
=7*2+5=19
②lg0.00001=lg10^(-5)=-5
5.①log 2 3乘上log 3 4乘上 4 5乘上log 3 2
=(lg3/lg2)(lg4/lg3)(lg5/lg4)(lg2/lg3)
=lg5/lg3
=log 3 5
②(log 4 3+log 8 3)(log 3 2+log 9 2)
=(1/2log 2 3+1/3log 2 3)(log 3 2 +1/2log 3 2)
=(5/6)log 2 3*(3/2)log 3 2
=5/4
6. ①若lg(x-y)+1g(x+2y)=1g2+1gx+1gy,求x/y的值
解：左边=lg(x-y)+1g(x+2y)=lg(x-y)(x+2y)=lg(x^2+xy-2y^2)
右边=1g2+1gx+1gy=lg(2xy)
故有：x^2+xy-2y^2=2xy
即 (x+y)(x-2y)=0
又x,y均为正数，
故只可能 x-2y=0,即x/y=2
②已知log 18 9=a,18^b=5,用a,b表示log 36 45
解：lg9/lg18=2lg3/(2lg3+lg2)=a
2lg3=2alg3+alg2
lg2=[(2-2a)/a]lg3
18^b=5
blg18=lg5
b(2lg3+lg2)=lg5
2lg3+lg2=2lg3/a
所以lg5=(2b/a)lg3
所以log36 45=lg45/lg36=(2lg3+lg5)/(2lg3+2lg2)
=[2lg3+(2b/a)lg3]/{2lg3+2[(2-2a)/a]lg3}
=[(2a+2b)/a]/[(4-2a)/a]
=(a+b)/(2-a)
1. a^m乘上a^n=______a^(m+n)_________,设M=a^m,N=a^n,所以MN=a^m乘上a^n=a^m+n.所以m+n=__loga(MN)______,又m=log a M,n=log a N,m+n=___log2(MN)______
所以log a (M乘上N）=_____m+n__________
注:我在a前面空了格,代表a是log的右下角的一个代数，聪明的都知道！
2.如果a>0,且a≠1，M>0,N>0,那么，
①log a(m乘上N)=___loga(m)+loga(N)____
②log a (M/N)=___loga(M)-loga(N)______
③log a M^n=___nloga(M)______(n∈R)
④log c a/log c b=_______logb(a)________
(a>0,且a≠1；c>0,且c≠1；b>0)
3.用log a x,log a y,log a z表示下列各式:
① log a xy/z=loga(x)+loga(y)-loga(z)
②log a （x^2乘上y的平方根/z的立方根)=2loga(x)+[loga(y)]/2-[loga(z)]/3
4.求下列各式的值:
①log 2 (4^7乘上2^5)=log2 (2^14*2^5)=log2(2^19)=19
②lg0.00001=lg10^(-5)=-5
5.利用对数的换底公式化简下列各式:
①log 2 3乘上log 3 4乘上 4 5乘上log 3 2
=(lg3/lg2)*(lg4/lg3)*(lg5/lg4)*(lg2/lg3)
=lg5/lg3
=log3 5
②(log 4 3+log 8 3)(log 3 2+log 9 2)
=(lg3/2lg2+lg3/3lg2)(lg2/lg3+lg2/2lg3)
=(lg3/lg2)*(lg2/lg3)*(1/2+1/3)*(1+1/2)
=(5/6)*(3/2)
=5/4
6.
①若lg(x-y)+1g(x+2y)=1g2+1gx+1gy,求x/y的值
(x-y)(x+2y)=2xy
x^2-xy-2y^2=0
(x-2y)(x+y)=0
x=2y,x=-y
由定义域，x>0,y>0
所以x=-y不成立
所以x=2y
x/y=2
②已知log 18 9=a,18^b=5,用a,b表示log 36 45
lg9/lg18=2lg3/(2lg3+lg2)=a
2lg3=2alg3+alg2
lg2=[(2-2a)/a]lg3
18^b=5
blg18=lg5
b(2lg3+lg2)=lg5
2lg3+lg2=2lg3/a
所以lg5=(2b/a)lg3
所以log36 45=lg45/lg36=(2lg3+lg5)/(2lg3+2lg2)
=[2lg3+(2b/a)lg3]/{2lg3+2[(2-2a)/a]lg3}
=[(2a+2b)/a]/[(4-2a)/a]
=(a+b)/(2-a)
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 ...
绛旓細鍥炵瓟锛1銆6.25=2.5*2.5,鎵浠og2.5(6.25)=2 2銆乴n[鏍瑰彿(e)]=0.5 3銆乴g[鏍瑰彿(2)]+lg[鏍瑰彿(5)]=lg[鏍瑰彿(10)]=0.5
绛旓細3.姒傚康 瀵规暟:___鑻^k=b,鍒欑Оk涓轰互a涓哄簳b鐨勫鏁___甯哥敤瀵规暟:___浠10涓哄簳鏁扮殑瀵规暟___鑷劧瀵规暟:___浠涓哄簳鏁扮殑瀵规暟___4.瀵规暟涓庢寚鏁伴棿鐨勫叧绯:___浜掍负閫嗚繍绠梍__5.鍒ゆ柇:x=10g 2 (-2) ( 閿 )x=10g 2 0 ( 閿 )6.10g a a=___1___ 10g a 1___0___...
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规瘮...
绛旓細鍘熷紡=lg5/lg2-2(lg10/lg4)=lg5/lg2-lg10/lg2=log2 (//2)=-1 鍘熷紡=lg4+lg5(lg20+lg5)=lg4+2lg5=lg4X25=lg100=2 鍘熷紡=lg2.4=lg24-1=lg3+3lg2-1=0.4771+0.9030-1=0.3801 lg鈭6=1/2lg6=1/2(lg3+lg2)=0.38905 ...
绛旓細涓銆佸凡鐭鐨勫鏁锛屾眰X 1. loga x=1/2loga m+2loga n loga x=logam^0.5+loga n ^2=loga n ^2*m^0.5 x=n^2(m)^0.5 2. loga x=2/3loga m-2loga n loga x=loga m^(2/3)-loga n^2 x=m^(2/3)/ n^2 浜屻佽绠楋細(1) 2^3+log2 5 = log2 2^3+log...
绛旓細lg x+lg y=2lg (x-2y)lgxy=lg(x-2y)^2 xy=(x-2y)^2=x^2-4xy+4y^2 x^2-5xy+4y^2=0 (x-4y)(x-y)=0 x=4y,x=y 瀹氫箟鍩燂紝x>0,y>0,x-2y>0 鏄剧劧x=y鏃讹紝x-2y<0 鎵浠=4y,x/y=4 log(鈭2) (x/y)=log(鈭2)(鈭2)^4=4 f(-1)=1-lga-2+lgb=-2 lga-1...
绛旓細=lg(25/9)+lg9-(lg(7/4)-lg7)=lg25-lg(1/4)=lg(25*4)=lg100 =2.(lg2)^2+lg2lg5+lg50 =(lg2)^2+lg2lg5+lg5+lg10 =(lg2)^2+lg2lg5+lg5+1.=lg2*(lg2+lg5)+lg5+1 =lg2+lg5+1 =lg(2*5)+1 =2.lg(5^2)+2/3lg8+lg5lg20+(lg2)^2 =2lg5+2lg2+lg...
绛旓細瑙ｇ瓟锛氳В锛氾紙1锛夆埖lg锛坙gy锛=lg3x+lg锛3-x锛=lg[3x锛3-x锛塢锛0锛渪锛3锛夛紝鈭磍gy=3x锛3-x锛夛紝鍗砯锛坸锛=10^[3x锛3-x锛塢锛泋鈭堬紙0锛3锛夛紙2锛夌敱锛1锛夌煡锛宖锛坸锛=10^[3x锛3-x锛塢锛泋鈭堬紙0锛3锛変护u=3x锛3-x锛=3锛3x-x²锛夊湪锛0锛3/2]涓婂崟璋冮掑锛屽湪[3/2锛3锕...
绛旓細1.x锛1og(2)3鎴杧锛21og(2)3锛3 鍘熷紡鍙啓鎴恖og(2)(2^x-1)log(2)4*(2^x-1)=3 鍙互瑙ｄ笂寮忓緱log(2)(2^x-1)=1鎴杔og(2)(2^x-1)=-3 瑙ｅ緱x锛1og(2)3鎴杧锛21og(2)3锛3 2.a=0.25,x=0.125 lgy=(lgx)^2/lga-3lgx+3lga,褰搇gx=1.5lga鏃讹紝y鍙栨渶澶у笺傚彲寰0....
