Question

log^2*100x-8lgx=4, пожалуйста, подробно

Answer 1

Смотри......................

Answer 2

ОДЗ : x > 0

$\displaystyle\bf\\lg^{2} 100x-8lgx=4\\\\\Big(lg100+lgx\Big)^{2} -8lgx-4=0\\\\\Big(2+lgx\Big)^{2} -8lgx-4=0\\\\4+4lgx+lg^{2} x-8lgx-4=0\\\\lg^{2} x-4lgx=0\\\\lgx\Big(lgx-4\Big)=0\\\\\\\left[\begin{array}{ccc}lgx=0\\lgx-4=0\end{array}\right \\\\\\\left[\begin{array}{ccc}lgx=0\\lgx=4\end{array}\right\\\\\\\left[\begin{array}{ccc}x_{1} =1\\x_{2} =10000\end{array}\right\\\\\\Otvet \ : \ 1 \ ; \ 10000$