Question

Calcule o valor de x na equação

Answer 1

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$\sf\dfrac{\sqrt{3}}{9}=\dfrac{{3}^{\frac{1}{2}}}{3^2}=3^{\frac{1}{2}-2}=3^{-\frac{3}{2}}\\\sf\dfrac{1}{27}=3^{-3}\\\sf\left(\dfrac{\sqrt{3}}{9}\right)^{2x-2}=\dfrac{1}{27}\\\sf (3^{-\frac{3}{2}})^{2x-2}=3^{-3}\\\sf 3^{-\frac{3\cdot(2x-2)}{2}}=3^{-3}\\\sf 3^{-3x+3}=3^{-3}\\\sf -3x+3=-3\\\sf-3x=-3-3\\\sf -3x=-6\cdot(-1)\\\sf 3x=6\\\sf x=\dfrac{6}{3}\\\huge\boxed{\boxed{\boxed{\boxed{\sf x=2 }}}}$