已知log23=a,log37=b试用a,b表示log(14)56
问题描述：
已知log23=a,log37=b试用a,b表示log(14)56
答
log(14)56=log(14)14*4=log(14)14+log(14)4=1+log(14)4
log(14)4=1/log(4)14=2/log(2)14=2/[log(2)7+1]=2/[log(2)3*log(3)7+1]=2/(ab+1)
log(14)56=1+2/(ab+1)
答
log(14)56=[log3(56)]/[log3(14)]=[3log3(2)＋log3(7)]/[log3(2)＋log3(7)]
=[(3/a)＋b]/[(1/a)＋b]=[ab＋3]/[ab＋1]