已知log5 (3)=a,log5(4）=b ,用a,b表示log5(24)

题目

已知log5 (3)=a,log5(4）=b ,用a,b表示log5(24)

答案

log5(4)=log5(2^2)=2log5(2)=b
log5(2)=b/2
log5(24) =log5(3*4*2)=log5(3)+log5(4)+log5(2)
=a+b+b/2
=a+3b/2