Logarithmic equation evaluation

First, simplify the terms: $\log_{\sqrt{3}}(x) = \log_{3^{1/2}}(x) = 2 \log_3(x)$

$\frac{\log_x(25)}{\log_x(0.008)} = \log_{0.008}(25) = \log_{5^{-3}}(5^2) = -\frac{2}{3}$

Substitute these into the equation: $2 \log_3(x) - \frac{2}{3} = \frac{16}{3}$ $2 \log_3(x) = 6 \implies \log_3(x) = 3$

Now, evaluate $\log_3(3x^2)$: $\log_3(3x^2) = \log_3(3) + 2 \log_3(x) = 1 + 2(3) = 7$