Question

Lg^2(10x)+lg(10x)= 6-3lg(1/x)

Answer 1

$lg^2(10x)+lg(10x)=6-3lg(\frac{1}{x} )\\x>0\\lg^2(10x)+lg(10x)=6-3(lg(1)-lg(x))\\lg^2(10x)+lg(10x)=6-3(-lg(x))\\(lg(10)+lg(x))^2+lg(10)+lg(x)=6+3lg(x)\\1+2lg(x)+lg^2(x)+1+lg(x)=6+3lg(x)\\2+lg^2(x)=6\\lg^2(x)=4\\lg(x)=2=>x=100\\lg(x)=-2=>x=100^{-1}$