Question

Log 3√3 =
1/9
me ajudem

Answer 1

$\mathrm{\ell og}_{\frac{1}{9}\,}(3\sqrt{3})=x\;\;\Rightarrow\;\;\left(\dfrac{1}{9} \right )^{x}=3\sqrt{3}\\ \\ \\ \left(\dfrac{1}{3^{2}} \right )^{x}=3\cdot 3^{1/2}\\ \\ \left(3^{-2} \right )^{x}=3^{1+(1/2)}\\ \\ 3^{-2x}=3^{3/2}\\ \\ \\ -2x=\dfrac{3}{2}\\ \\ x=-\dfrac{3}{4}\;\;\Rightarrow\;\;\boxed{ \begin{array}{c} \mathrm{\ell og}_{\frac{1}{9}\,}(3\sqrt{3})=-\dfrac{3}{4} \end{array} }$