Question

Нужно решить одно задание под цифрой 2. 

Answer 1

log₃5=a
2*log₃225-log₅45-2*log₁₅25
1. 2*log₃225=2*log₃(25*9)=2*(log₃25+log₃9)=2*(log₃5²+log₃3²)=
=2*(2*log₃5+2*log₃3)=2*(2a+2)=4a+4.
2. log₅45=log₅(5*9)=log₅5+log₅9=1+log₅3²=1+2*log₅3=1+2/log₃5=1+2/a.
3. 2*log₁₅25=2*log₁₅5²=2*2*log₁₅5=4*log₁₅5=4/log₅15=4/log₅(5*3)=
=4/(log₅5+log₅3)=4/(1+1/log₃5)=4/(1+1/a)=4/((1+a)/a)=4a/(1+a).
4. 4a+4-(1+2/a)-4a/(1+a)=4a+4-1-2/a-4/(1+a)=4a+3-2/a-4/(1+a).
Ответ: Е.