Question

Помогите с логарифмами!!!!

Answer 1

$lgx ^{ \frac{lgx+11}{6} }=lg 10 ^{lgx+1}\\\\ \frac{lgx+11}{6}*lgx=(lgx+1)lg10\\\\(lgx+11)lgx =6(lgx+1)\\\\lg ^{2}x+11lgx-6lgx-6=0\\\\lg ^{2} x+5lgx-6=0$
По теореме обратной теореме Виетта:
lgx₁ = - 6                       lgx₂ = 1                ОДЗ: x > 0
$x _{1}=10 ^{-6} =0,000001\\\\x _{2} =10$