The solution of the equation 2lgx LG (x-1) = 2 (1-lg5) is?

The solution of the equation 2lgx LG (x-1) = 2 (1-lg5) is?


2lgx-lg(x-1)=2(1-lg5)
lgx^2-lg(x-1)=2(lg10-lg5)
lg[x^2/(x-1)]=2lg2
lg[x^2/(x-1)]=lg4
x^2/(x-1)=4
x^2-4x+4=0
(x-2)^2=0
x=2



Solving (lg5) ^ 2 + LG50 * LG2
It's better to write down every step


(lg5)^2+lg50*lg2
=(lg5)^2+(lg25+lg2)*lg2
=(lg5)²+lg5²lg2+(lg2)²
=(lg5)²+2lg5lg2+(lg2)²
=(lg5+lg2)²
=(lg10)²
=1²
=1



Equation LG2 times lgx = lg5


lg2×lgx = lg5
lgx = lg5/lg2
x = 10^(lg5/lg2)
x = (10^lg5)^(1/lg2)
x = 5^(1/lg2)