设log8^9=a,log3^5则lg2=

备注：第一个（）内是“底数”,第二个（）内是“真数”log8底9*log3底32=log（3的平方）（2的三次方）*log（2的五次方）（3)=3/2log(3)(2)*1/5log(2)(3)=3/

答案是10/3

log(8)3=lg3/3lg2=a,log(3)5=lg5/lg3=b,lg2+lg5=1lg5=3ab/(1+3ab)

log(8)9=lg9/lg8=2lg3/3lg2=a,lg2=2lg3/3a.log(3)5=lg5/lg3=b,lg3=lg5/b.lg5+lg2=lg10=1所以,lg2=2/(3ab+2)

log89=lg9/lg8=2lg3/3lg2=a;log320=lg20/lg3=(1+lg2)/lg3=b;从此建立二元一次方程组,解得lg2=2/(3ab-2),

7*(2/3)log2(3)=alog2(3)=3a/14log3(2)=14/(3a)log3(5)=blg2=log3(2)/log3(10)=log3(2)/[log3(2)+log3(5)]=

log827*log316=log23*log32*4=4

log8(9)=a用换底公式lg9/lg8=2lg3/3lg2=a2lg3=3alg2log3(5)=blg5/lg3=blg3=lg5/b2lg5/b=3alg2lg5=lg(10/2)=1-lg2

log89=2/3log23=mlog23=1.5mlog23*log35=log25=3/2*mnlog512=log5(2*2*3)=2*log52+log53=2*2/(3mn)+1/n=(4+

=(lg2/lg3)*(lg9/lg8)(换底）=(lg2*lg9)/(lg3*lg8)=(lg2*2lg3)/(lg3*3lg2)=2/3

a=(lg3)/(lg8)b=(lg5)/(lg3)ab=lg8/lg5=(3lg2)/(lg5)=3(lg(10/5)/(lg5))=3(lg10-lg5)/lg5=3(1-lg5)/lg5所以lg

log8(9)=a8^a=92^3a=3^23a*lg2=2*lg3log3(5)=b3^b=5b*lg3=lg53a*lg2=2*lg5/b=2(1-lg2)/b(3ab+2)lg2=2lg2=2/

log83=p,lg3/lg8=p.log35=q,lg5/lg3=q.两式相乘得:lg5/lg8=pq.因lg8=lg2^3=3lg2=3×（1-lg5）所以lg5/[3×（1-lg5）]=pq.l

即p=lg3/lg8q=lg5/lg3所以pq=lg5/lg8=lg5/3lg2=lg5/[3(1-lg5)]所以lg5=3pq+pqlg5lg5=-3pq/(pq-1)

上面的计算似乎不对可以这样算p=log(8)3=log(2^3)3=1/3log(2)3=1/3lg3/lg2(换底公式）q=log(3)5=lg5/lg3上面两式相乘有pq=1/3(lg5/lg2)

a=log89=lg9/lg8=2lg3/3lg2b=log320=lg20/lg3=(1+lg2)/lg3ab=2(1+lg2)/3lg2=(2/3lg2)+1/3ab-1/3=2/3lg2lg2=

见图

log83=a==>8^a=3log35=b==>3^b=58^(ab)=52^(3ab)=5∴log25=3ab2^(3ab+1)=10所以log210=3ab+1∵lg5=log105=(log2

哦.由已知可得：log8(3)=lg3/lg8=lg3/(3lg2)=a,log3(5)=lg5/lg3=b所以：[lg3/(3lg2)]×(lg5/lg3)=ab即lg5/(3lg2)=ablg5=

换底公式lg4/lg3*lg8/lg4*lgm/lg8=log4(4²)lgm/lg3=2lgm=2lg3=lg9m=9