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

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

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

log5(24) =log5(4)+log(6)=log5(4)+log5(3)+log5(2)=a+b+log5(2)
log5(4)=log5(2)+log5(2)
所以log5(2)=b/2
所以log5(24)=a+3/2*b

a+1.5b