Log37=m,log23=n,求log4256

题目

Log37=m,log23=n,求log4256
log37中的3在右下方log23中的3在右下方log4256中的42在右下方

答案

换底公式:loga(b）=logn(b)/[logn（a）]
log2(3)=n,
log3(3)/log3(2)=n
1/log3(2)=n
log3(2)=1/n;
log42(56)=log3(56)/log3(42)
=log3(7*2³)/log3(7*2*3)
=[log3(7)+log3(2³)]/[log3(7)+log3(2)+log3(3)]
=[m+3log3(2)]/[m+1/n+1]
=[m+3/n]/[(mn+n+1)/n]
=(mn+3)/(mn+n+1)