Question

简单的对数题几枚已知log2 3=a，log3 7=b试用a b表示log14 56比较大小 log6 7 log7 6

Answer 1

log2 3=a ----->log3 2=1/a

log3 7=b

log3 (56)=log3(7*2^3)=log3(7)+3log3(2)=b+3/a=(ab+3)/a

log3(14)=log3(7*2)=log3(7)+log3(2)=b+1/a=(ab+1)/a

所以,由换底公式,log14 56=log3 (56)/log3(14)=(ab+3)/(ab+1)