Question

$( frac{ sqrt{10} }{3})^{3 x^{2} -3}= 0,81^{-2x}$

Answer 1

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

$0,81=frac{81}{100}=frac{3^4}{10^2}$