Question

решите плиз lg2x-3lgx-4=0

Answer 1

Ответ:

0,1 ;

10000.

Объяснение:

$lg^{2}x-3lgx-4=0$

Замена: lgx=t.

$t^{2} -3t-4=0\\t_{1} =4, t_{2} =-1,\\lgx=4, x=10000,\\lgx=-1, x=0,1.$

Answer 2

ОДЗ : x > 0

$\lg^{2}x-3lg x-4=0\\\\\lg x=m\\\\m^{2} -3m-4=0\\\\D=(-3)^{2} -4\cdot(-4)=9+16=25=5^{2}\\\\m_{1}=\frac{3-5}{2} =-1\\\\m_{2} =\frac{3+5}{2}=4\\\\1) \lg x=-1\\\\x=10^{-1} =0,1\\\\2)\lg x=4\\\\x=10^{4} =10000\\\\Otvet:\boxed{0,1 \ ; \ 10000}$