杭州交通信息网梦三国典韦视频:一道高一数学奥赛题~
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lg(1+1/7)=a lg(1+1/49)=b
用a,b表示 lg2
用a,b表示 lg2
a = lg(1 + 1/7)
= lg(8/7)
= 3lg2 - lg7
b = lg(1 + 1/49)
= lg(50/49)
= lg(100/2) - 2lg7
= 2 - lg2 - 2lg7
2a - b
= (6lg2 - 2lg7 ) - (2 - lg2 - 2lg7)
= 7lg2 - 2
lg2 = (2a - b + 2)/7
a = lg(1 + 1/7)
= lg(8/7)
= 3lg2 - lg7
b = lg(1 + ¼9)
= lg(50/49)
= lg(100/2) - 2lg7
= 2 - lg2 - 2lg7
2a - b
= (6lg2 - 2lg7 ) - (2 - lg2 - 2lg7)
= 7lg2 - 2
lg2 = (2a - b + 2)/7