Задача 30660 log4100+log212-2log2sqrt(30)+4log34...

89648013987

2018-10-30 19:57:25

log4100+log212-2log2sqrt(30)+4log34

sova

2018-10-30 21:20:01

★

log_(4)100=log_(2^2)10^2=(2/2)log_(2)10=log_(2)10;
2log_(2)sqrt(30)=log_(2)(sqrt(30))^2=log_(2)30;
3^(log_(3)4)=4

тогда

log_(4)100+log_(2)12-2log_(2)sqrt(30)+3^(log_(3)4)=

=log_(2)10+log_(2)12-log_(2)(30) +4=

=log_(2)(10*12)/(30) +4= log_(2)4+4=2+4=6