{高一数学}对数的运算,请教几道题。在线等！！！！！！！！！！~~~~~~ 高一数学对数的运算 化简2道题
\u5e2e\u5fd9\u89e3\u51e0\u4e2a\u9ad8\u4e00\u51fd\u6570\u6570\u5b66\u9898\uff08\u9ad8\u5206\uff0c\u5728\u7ebf\u7b49~\uff01\uff01\uff01\uff091. x-1>0\uff0c
3-x>0
\u52191<x<3.
(2+b)/2<x<b+1,
B\u662fA\u7684\u5b50\u96c6\uff0c\u5f53B\u4e3a\u7a7a\u96c6
b+1\u2264(2+b)/2,\u5373b\u22640
B\u4e0d\u4e3a\u7a7a\u96c6\u65f6\uff0c
b>0\uff0c\u4e14b+1\u22643\u4e141\u2264(2+b)/2\uff0c
\u5f97\uff1a0<b\u22642
\u7efc\u5408\u5f97\uff1ab\u22642
2.\u51fd\u6570\u5f00\u53e3\u5411\u4e0a\uff0c\u4e14\u8fc7\uff080\uff0c2\uff09\u70b9\uff0c
\u6240\u4ee5\u6ee1\u8db3\u5df2\u77e5\u6761\u4ef6\u5e94\u8be5\u662f\uff1a\u25b3>0,\u5bf9\u79f0\u8f74\u5728y\u8f74\u53f3\u4fa7\uff1a-b/2a>0,\u89e3\u5f97\uff1aa<-\u221a2
\uff082\uff09f(x+1)=f(1-x),\u5373\u5bf9\u79f0\u8f74\u662fx=1\uff0c\u6240\u4ee5a=-1\uff0c\u5f00\u53e3\u5411\u4e0a\uff0c
\u5728x=-5\u5904\u53d6\u5f97\u6700\u5927\u503c\uff1a37\uff1b\u5728x=1\u5904\u53d6\u6700\u5c0f\u503c\uff1a1
\uff083\uff09\u8981\u8ba8\u8bba\u5bf9\u79f0\u8f74\u548c\u533a\u95f4\u7684\u5173\u7cfb\uff0c\u5bf9\u79f0\u8f74\u4e3a\uff1ax=-a,\u5f00\u53e3\u5411\u4e0a\u3002
-a\u2264-5\uff0c\u5373a\u22655\u65f6\uff0c\u5bf9\u79f0\u8f74\u5728\u533a\u95f4\u7684\u5de6\u4fa7\uff0c\u2234\u5728x=-5\u65f6\u53d6\u5f97\u6700\u5c0f\u503c\uff1a27-10a
-5<-a<5,\u5373-5<a<5\u65f6\uff0c\u5bf9\u79f0\u8f74\u5728\u533a\u95f4\u5185\uff0c\u5728x=-a\u65f6\u53d6\u5f97\u6700\u5c0f\u503c\uff1a2-a²
-a\u22655\uff0c\u5373a\u2264-5\u65f6\uff0c\u5bf9\u79f0\u8f74\u5728\u533a\u95f4\u53f3\u4fa7\uff0c\u5728x=5\u65f6\u53d6\u5f97\u6700\u5c0f\u503c\uff1a27+10a
3.
h(-x)=loga (1-x)-loga (1+x)=-h(x),
\u5219h(x)\u4e3a\u5947\u51fd\u6570
f(3)=2,
\u5219loga4=2
\u5219a=2
h(x)>0\uff0c\u5373loga (1+x)-loga (1-x)=loga(1+x)/(1-x)>0
\u800ca>1,
\u5219(1+x)/(1-x)>1
\u4e14\u8981\u4f7f\u5f97\u5bf9\u6570\u51fd\u6570\u6709\u610f\u4e49\uff0c\u5219
1+x>0
1-x>0
\u52190<x<1
4.y=g(mx^2+2x+m)\u7684\u503c\u57df\u4e3aR,\u5373
log1/3 (mx^2+2x+m) \u503c\u57df\u4e3aR
\u53ef\u77e5\u6709mx^2+2x+m>=0
\u5f53m\u22600\u65f6
\u6240\u4ee5\u25b3>=0
\u52194-4m^2>=0
\u5219-1>=m>=1
\u5f53m=0\u65f6\uff0c\u4ecd\u7136\u6210\u7acb
\u51fd\u6570y=[f(x)]^2-2af(x)+3\u7684\u6700\u5c0f\u503ch(a)
y=[f(x)-a]^2+3-a^2
\u5f53a<1/3\uff0c\u5219\u53ef\u77e5\u5728x=1\u65f6\u3002\u53d6\u5f97\u6700\u5c0f\u503c:4-2a
\u5f531/3<=a<=3\uff0c\u5219\u53ef\u77e5\u5728x=log1/3 a\u65f6\u3002\u53d6\u5f97\u6700\u5c0f\u503c3-a^2
\u5f53a>3\uff0c\u5219\u53ef\u77e5\u5728x=-1\u65f6\u3002\u53d6\u5f97\u6700\u5c0f\u503c:4+2a
\u51fd\u6570y=g[f(x^2)]\u7684\u5b9a\u4e49\u57df\u4e3a[m,n],\u503c\u57df\u4e3a[2m,2n],
\u5373y=x^2
\u5219\u53ef\u80fd\u4e3a\uff1a
m>=0
\u5219\uff0c\u53ea\u80fd\u4e3a\uff1a
2m=m^2
2n=n^2
\u5219m=0\uff0cn=2
\u6216\u8005
n<0
\u5219\uff0c\u53ea\u80fd\u4e3a\uff1a
2m=n^2
2n=m^2
\u65e0\u89e3
m0
\u5219\u3002
\u6700\u5c0f\u503c\u4e3ax=0 ,\u53732m=0, m=0
\u4e0d\u6ee1\u8db3\uff0c\u820d\u53bb
y=log1/2 (x^2-2x+5)\u7684\u503c\u57df
x^2-2x+5=(x-1)^2+4
\u800c(x-1)^2+4 \u5f53x=1\u53d6\u5f97\u6700\u5c0f\u503c4
\u800cy=log1/2 (x^2-2x+5)\uff0c\u6307\u65701/2<1,\u51fd\u6570\u5355\u51cf\u3002
\u6240\u4ee5y=log1/2 (x^2-2x+5)\u6709\u6700\u5927\u503c
y=log1/2 4=-2
\u6240\u4ee5\u503c\u57df\u4e3a[-\u221e\uff0c-2]
\u5e26\u51651\uff0c\u33d11+2-3=-1<0
\u5e26\u51652\uff0c\u33d12+4-3=l.3>0
\u5219\u6839\u5fc5\u5728B(1,2)
1.\u4e3a\u4e86\u6253\u5b57\u65b9\u4fbf\uff0c\u6211 \u5148\u8bbea=lg5,b=lg2
\u90a3\u4e48\u6709a+b=lg(5*2)=1
\u6240\u4ee5\u539f\u5f0f=a³+3ab+b³
=(a+b)(a²-ab+b²)+3ab
=1*\uff08a²-ab+b²)+3ab
=(a+b)²
=1
2.\u8fd9\u91cc\u6253\u4e0d\u4e0a\u5e95\u6570\uff0c\u6545\u7565\u53bb\u4e86\uff0c\u4f60\u5199\u7684\u65f6\u5019\u518d\u8865\u4e0a\u5427\u3002O(\u2229_\u2229)O
\u7b2c\u4e00\u4e2a\u5bf9\u6570=1/2log7-1/2log48
\u7b2c\u4e8c\u4e2a\u5bf9\u6570=1/2log144
\u7b2c\u4e09\u4e2a\u5bf9\u6570\u4e0d\u53d8
\u90a3\u4e48\u539f\u5f0f=1/2\uff08log7-log48+log144-log42\uff09
=1/2log[(7*144)/(48*42)]
=1/2log(2^-1)
=-1/2long2
=-1/2
=(11/5)lg3/(lg3)
=11/5；
（2）原式=[(2lg3)/(3lg2)]*[(5lg2)/(lg3)] (应用对数换底公式)
=10/3；
（3）原式=(lg5+lg7)/lg5+lg2/(-lg2)+(2lg5+lg2)/lg5-(lg7+lg2)/lg5 (应用对数换底公式)
=3lg5/lg5-1
=3-1
=2；
（4）原式=(2lg3)/(lg3/2)+(3lg3)/(2lg3)+(1/4)^[(-4lg2)/(2lg2)] (应用对数换底公式)
=4+3/2+4²
=43/2。
过程在图片中，细节自己推一下
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