To solve this equation, we'll first simplify it by applying the properties of logarithms.

0.5 lg* lg(0.001x) = lg(0.1)

First, we can combine the first two logarithms using the properties of logarithms:

lg*(lg(0.001x)) = 2lg(0.1)

Now we can rewrite the equation as:

lg(lg(0.001x)) = 2lg(0.1)

Next, we can apply the property of logarithms that states lg(a) = b is equivalent to 10^b = a:

lg(0.001x) = 10^(2lg(0.1))

lg(0.001x) = 10^(lg(0.1)^2)

lg(0.001x) = 10^(2)

lg(0.001x) = 10

Finally, we can solve for x:

0.001x = 10

x = 10000

Therefore, the solution to the equation is x = 10000.