To solve this logarithmic equation, we first need to simplify the left side using properties of logarithms:

lg 3x - lg 9x + lg 81x = 3/4

We can apply the properties of logarithms to combine the terms:

lg (3x * 81x / 9x) = 3/4
lg (243x^2 / 9x) = 3/4
lg (27x) = 3/4

Now, to eliminate the logarithm, we rewrite the equation in exponential form:

27x = 10^(3/4)
27x = 5√10

x = 5√10 / 27

Thus, the solution to the logarithmic equation lg 3x - lg 9x + lg 81x = 3/4 is x = 5√10 / 27.