$7.66 x^{2 \lg ^{2} x}=10 x^{3}$.
7.66 Instruction. Take the logarithm of both sides of the equation to the base 10 and solve the resulting cubic equation by factoring.

Answer: $x_{1}=0.1, x_{2,3}=10^{0.5(1 \pm \sqrt{3})}$.