已知log(a)x=1,log(b)x=2,log(c)x=4,则log(abc)x=?

已知log(a)x=1,log(b)x=2,log(c)x=4,则log(abc)x=?
已知log(a)x=1,log(b)x=2,log(c)x=4,则log(abc)x=?

已知log(a)x=1,log(b)x=2,log(c)x=4,则log(abc)x=?
log(a)x=1
lgx/lga=1
lga/lgx=1
log(b)x=2
lgx/lgb=2
lgb/lgx=1/2
log(c)x=4
lgx/lgc=4
lgc/lgx=1/4
所以lga/lgx+lgb/lgx+lgc/lgx
=1+1/2+1/4=7/4
而lga/lgx+lgb/lgx+lgc/lgx
=(lga+lgb+lgc)/lgx
=lg(abc)/lgx=7/4
log(abc)x=lgx/lg(abc)
=1/[lg(abc)/lgx]
=1/(7/4)
=4/7

结果是1/8，log(a)x=logx／loga＝1 同理，log(abc)x＝logx／logabc＝1/8

因log(a)x=1,则a=x
同理log(b)x=2,则b^2=x
log(c)x=4,则c^4=x
所以，a=b^2=c^4
则,abc=c^7
所以，log(abc)x=log(c^7)x=(1/7)log(c)x
又x=c^4,
即,原式=(1/7)log(c)(c^4)=(4/7)log(c)c
(因log(c)c=1)
=4/7

因为log(a)x=1,
log(b)x=2,
log(c)x=4,
所以 a=x；b*b=x；c*c*c*c=x；
a*b*c=c的7次方
所以 log(abc)x=log（1又3/4*x）x=1.75