Log5(30)/log30(5)-log5(150)/log6(5) - вопрос №7755588530305515065 от sasha123123476 06.04.2021 09:10

Question

Математика: Log5(30)/log30(5)-log5(150)/log6(5)

sasha123123476 · Answer

Log(5)30=log(5)(5*6)=log(5)5+log(5)6=1+log(5)6
log(30)5=1/log(5)30=1/(1+log(5)6)
log(5)150=log(5)(25*6)=log(5)25+log(5)6=2+log(5)6
log(6)5=1/log(5)6
получим
(1+log(5)6):1/(1+log(5)6)-(2+log(5)6):1/log(5)6=
=(1+log(5)6)²-(2+log(5)6)*log(5)6=
=1+2log(5)6+log²(5)6-2log(5)6-log²(5)6=1