log2(3)=a log3(7)=b 那么log14(56)=多少?

题目

log2(3)=a log3(7)=b 那么log14(56)=多少?

答案

log2(3)=a 3=2^a log3(7)=b 7=3^b=(2^a)^b=2^(a×b) log2(7)=a×b log14(56)=log14(14×4)=log14(14)+log14(4)=1+2log14(2)=1+2[log2(2)]/[log2(14)] =1+2/log2(14)=1+2/log2(2×7)=1+2/[log2(2)+log2(7)]=1+2/(1+a...