Question

Надо решить #5,6,7, желательно решение на фото с листка.

Answer 1

5)log(30)3=a⇒log(2)3/(1+log(2)3+log(2)5)=a⇒1+log(2)3+log(2)5=log(2)3/a  (1)
log(30)5=b⇒log(2)5/(1+log(2)3+log(2)5)=b⇒log(2)5=b*log(2)3/a  (2)
1+log(2)3+b*log(2)3/a =log(2)3/a  ⇒a+alog(2)3+blog(2)3=log(2)3⇒a=log(2)3(1-a-b)⇒
⇒log(2)3=a/(1-a-b)
log(30)8=3/(1+log(2)3+log(2)5)=3:log(2)3/a=3a/log(2)3=3a:a/(1-a-b)=3a*(1-a-b)/a=3(1-a-b)
6)log(14)7=a⇒log(2)7/(1+log(2)7=a⇒log(2)7=a/(1-a)
log(14)5=b⇒log(2)5/(1+log(7)=b⇒log(2)5=blog(2)7/a=b/(1-a)
log(35)28=(2+log(2)7)/(log(2)5+log(2)7)=(2+a/(1-a)):(a/(1-a)+b/(1-a))=
=(2-a)/(1-a)*(1-a)/(a+b)=(2-a)/(a+b)
7)log(0,5)sin70*sin50*sin10=log(0,5)sin10cos20cos40=
=log(0,5)[sin10cos10cos20cos40/cos10]=log(0,5)[sin20cos20cos40/2cos10]=
=log(0,5)[sin40cos40/4cos10]=log(0,5)[sin80/8cos10]=log(0,5)[cos10/8cos10]=
=log(0,5)[1/8]=3