Задача 30589 log2225 - 2/log52 - log29 ......

89648013987

2018-10-28 13:42:54

log2225 - 2/log52 - log29 ...

sova

2018-10-28 14:00:32

★

Так как
log_(2)5=1/log_(5)2
log_(9)25=log_(3^2)5^2=(2/2)*log_(3)5
и
5^(1/log_(3)5)=5^(log_(5)3)=3

log_(225)-2*log_(2)5 -log_(2)9+ 5^(log_(5)3)=

=log_(2)225-log_(2)5^2-log_(2)9 + 3=

=log_(2) (225/(25*9))+3= log_(2)1+3=0+3=3
О т в е т. 3