To solve this equation, we can first simplify it by using the properties of logarithms:

lgx + lg$0.001x$ = lg0.01

lg$x\ast 0.001x$ = lg0.01

lg$0.001x^2$ = lg0.01

Now, we can remove the logarithm by using 10 as the base:

0.001x^2 = 0.01

Now, we can solve for x:

0.001x^2 = 0.01

x^2 = 0.01 / 0.001

x^2 = 10

x = √10

Therefore, the solution to the equation lgx + lg$0.001x$ = lg0.01 is x = √10.