[latex]( \frac{ \sqrt{10} }{3})^{3 x^{2} -3}= 0,81^{-2x} [/latex]

[latex](\frac{\sqrt{10}}{3})^{3x^2-3}=0,81^{-2x}\\\\\frac{10^{\frac{3x^2-3}{2}}}{3^{3x^2-3}}=\frac{3^{-8x}}{10^{-4x}}\\\\10^{\frac{3x^2-3}{2}-4x}=3^{-8x+3x^2-3x}\\\\(\sqrt{10})^{3x^2-8x-3}=3^{3x^2-8x-3}\\\\(\frac{\sqrt{10}}{3})^{3x^2-8x-3}=1,\; \; 1=(\frac{\sqrt{10}}{3})^0\\\\3x^2-8x-3=0\\\\x_1=-\frac{1}{3},\; x_2=3[/latex] [latex]0,81=\frac{81}{100}=\frac{3^4}{10^2}[/latex]