已知log以6为底7=a
log以3为底4=log3 2²=2log3 2=b
所以log3 2=b/2
则log以14为底21
=log6 21/log6 14
=(log6 7+log6 3)/(log6 7+log6 2)
=[a+log3 3/log3 6]/[a+log3 6/log3 2]
=[a+1/(log3 3+log3 2)]/[a+(log3 3+log3 2)/(b/2)]
=[a+1/(1+b/2)]/[a+(1+b/2)/(b/2)]
=[a+2/(b+2)]/[a+(b+2)/b]