(log_(2)8+log_(c)ab)/(log_(c)\sqrt(ab)+log_(3)\sqrt(27)) Чему численно равно выражение?

Question

(log_(2)8+log_(c)ab)/(log_(c)\sqrt(ab)+log_(3)\sqrt(27))
Чему численно равно выражение?

Answer 1

1) log₂8+log(c)ab=log₂2³+log(c)ab=3+log(c)ab=log(c)c³+log(c)ab=log(c)abc³.

2) log(c)√ab+log₃√27=log(c)√ab+log₃3³/²=log(c)√ab+3/2=log(c)√ab+log(c)c³/²=

=log(c)√ab+log(c)√c³=log(c)√abc³=log(c)(abc³)¹/²=(1/2)*log(c)abc³

3) log(c)abc³/((1/2)*log(c)abc³)=1/(1/2)=2.