log3 2=a,则log6 根号24等于?

题目

log3 2=a,则log6 根号24等于?

答案

log6 根24
=1/2 log6 24
=1/2 log6 (4x6)
=1/2 (log6 4 + log6 6)
=1/2 + 1/2 log 6 4
=1/2 + log6 2
=1/2 + log3 2/log3 (2x3)
=1/2 + (log3 2)/(log3 2 + log3 3)
=1/2 + a/(a+1)
=(2a+1)/(2a+2)