Find out x if lgx = -lg2.

To find out x, first we'll have to impose constraints of existence of logarithms:

x>0

lg x=-lg 2

lg x = lg [(2)^-1]

lg x = lg 1/2

We'll use the one to one property of logarithms:

x = 1/2

Because of the fact that the solution is positive, it's convenient, so

x=1/2