7log8^9=a log3^5=b 求lg2 lg3 lg5
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7log8^9=a log3^5=b 求lg2 lg3 lg5
![7log8^9=a log3^5=b 求lg2 lg3 lg5](/uploads/image/z/3040763-59-3.jpg?t=7log8%5E9%3Da+log3%5E5%3Db+%E6%B1%82lg2+lg3+lg5)
7 *(2/3)log2(3)=a
log2(3)=3a/14
log3(2)=14/(3a)
log3(5)=b
lg2=log3(2)/log3(10)=log3(2)/[log3(2)+log3(5)]=[14/(3a)]/[14/(3a)+b]=14/(14+3ab)
lg3=1/log3(10)=1/[log3(2)+log3(5)]=1/[14/(3a)+b]=3a/(14+3ab)
lg5=1-lg2=1- 14/(14+3ab)=3ab/(14+3ab)
log2(3)=3a/14
log3(2)=14/(3a)
log3(5)=b
lg2=log3(2)/log3(10)=log3(2)/[log3(2)+log3(5)]=[14/(3a)]/[14/(3a)+b]=14/(14+3ab)
lg3=1/log3(10)=1/[log3(2)+log3(5)]=1/[14/(3a)+b]=3a/(14+3ab)
lg5=1-lg2=1- 14/(14+3ab)=3ab/(14+3ab)