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