log14为底7=a,14的b次方=5

运用换底log14(56)=log3(56)/log3(14)=log3(7*8)/log3(2*7)=〔log3(7)＋log3(8)〕/〔log3(7)＋log3(2)〕log3(2)=1/log

根号则2b-14>=0,b>=77-b>=0,

根号下大于等于014-2b>=0,b=0,b>=7同时成立则b=7所以14-2b=0,b-7=0所以a=0+0+3=3a-b=-4所以原式=√(-4)²=√16=4

log23=a;log37=b即lg3/lg2=a;lg7/lg3=b;所以lg7/lg2=a*b所以log72=1/a*b同理log142=1/1+ab;所以结果为（3+ab）/(1+ab)

log23=lg3/lg2=a,所以lg3=alg2,同理：log37=lg7/lg3=b,所以lg7=blg3即lg7=ab*lg2log1456=lg56/lg14其中lg56=lg7+lg8=l

运用换底:log14(56)=log3(56)/log3(14)=〔log3(7)＋log3(8)〕/〔log3(7)＋log3(2)〕log3(2)=1/log2(3)=1/alog3(8)=3lo

答：ab=log2^7ab+1=log2^7+1=log2^14ab+3=log2^7+3=log2^56log14^56=(ab+3)/(ab+1)

log14^56=log3^56/log3^14=(log3^7+3log3^2)/(log3^7+log3^2)=(b+3/a)/(b+1/a)=(3+ab)/(1+a)

若log23=a,log37=b则log23*log37=ab即log27=ablog1456=log214/(log256)=(log22*7)/(log27*8)=(log22+log27)/(l

根据题意a+b=√7b=√7-a2²＜7＜3²所以√7的整数部分为2,即a=2a-b=a-(√7-a)=2a-√7=2×2-√7=4-√7

因为：|a-3|+|b+7|=0|a-3|≥0,|b+7|≥0所以a-3=0,b+7=0a=3,b=-7（a+b)[-a-(-b)]=(b+a)(b-a)=(-7+3)(-7-3)=40

log14(2)=alog2(14)=1/a=log2(2)+log2(7)log2(7)=1/a-1log√2(7)=2(1/a-1)

运用换底:log14(56)=log3(56)/log3(14)=〔log3(7)＋log3(8)〕/〔log3(7)＋log3(2)〕log3(2)=1/log2(3)=1/alog3(8)=3lo

(1)由换底公式得到log14^7=ln7/ln14=ln7/(ln2+ln7)=a;故ln7=aln2+aln7;解得ln7=aln2/(1-a);14^b=5.故log14^5=b.即ln5/(l

a=lg3/lg2lg2=lg3/ab=lg7/lg3lg7=blg3log1456=lg56/lg14=(lg7+lg8)/(lg7+lg2)=(lg7+3lg2)/(lg7+lg2)=(blg3+

由换底公式：log14(2)=lg2/lg14log√2(7)=lg7/lg√2lg√2=(lg2)/2所以log√2(7)=lg7/lg√2=2lg7/lg2而：log14(2)=lg2/lg14=

第二题,做出来了!1.log147=lg7/lg14log145=lg5/lg14A=lg7/lg14=lg7/(lg7+lg2)B=lg5/lg14=(1-lg2)/(lg7+lg2)通过以上两式可

log35^2=log35^14-log35^7=1/(a+b)-1/log7^35=1/(a+b)-1/(1+b/a)=(1-a)/(a+b)原式=(1+1-a)/(a+b)=(2-a)/(a+b)

用换底公式求即可.log35（28）=log14(28)/log14(35)=[log14(14)+log14(2)]/[log14(7)+log14(5)]=[1+1-log14(7)]/[log1

log23=a----->log32=1/alog37=blog3(56)=log3(7*2^3)=log3(7)+3log3(2)=b+3/a=(ab+3)/alog3(14)=log3(7*2)=