对数函数
已知log2 3=a ,log3 7=b,试用a,b表示log14 56
log(14)56=lg56/lg14=(lg7+3lg2)/(lg2+lg7) =(log(2)7+3log(2)2)(log(2)2+log(2)7) =(ab+3)/(1+ab)
首先log7=(log3)*[(log7)/(log3)]=(log3)*(log7)=ab。 其次log56=(log56)/(log14) =[log(8*7)]/[log(2*7)] =(3+log7)/(1+log7) =(3+ab)/(1+ab)
log3 7=log2 7/log2 3=log2 7/a=b log2 7=ab log14 56=log2 56/log2 14=log2(7×8)/log2 (2×7)= =(log2 7+3log2 2)/(log2 2+log2 7)=(ab+3)/(1+ab)=(3+ab)/(1+ab)
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