Question

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

Answer 1

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