Question

Log16(42)*log7(8)-3log49корень из 6

Answer 1

log16(42)=log7(42)/log7(16)=(log7(7)+log7(6))/log7(2^4)=(1+log7(6))/4log7(2)
log7(8)=log7(2^3)=3log7(2)
Log16(42)*log7(8)=(1+log7(6))/4log7(2)*3log7(2)=3/4(1+log7(6))=3/4+3/4*log7(6)
3log49(√6)=3*log7(6^(1/2))/log7(49)=3*1/2*log7(6)/2=3/4*log7(6)
3/4+3/4*log7(6)-3/4*log7(6)=3/4
Ответ: 3/4