1/(lg x + lg 0,1)+1/lg x = 3/2

Question

1/(lg x + lg 0,1)+1/lg x = 3/2

Answer 1

1/(lgx-1)+1/lgx=3/2
3lg²x-3lgx-2lgx-2lgx+2=0
3lg²x-7lgx+2=0
a=lgx
3a²-7a+2=0
D=49-24=25 √D=5
a1=(7-5)/6=1/3⇒lgx=1/3⇒x=∛10
a2=(7+5)/6=2⇒lgx=2⇒x=100