Question

calcule o seguinte logaritmo log 3raiz de 3 1/9

Answer 1

$\log_{3\sqrt3}\left(\dfrac19\right)=x\\\\(3\sqrt3)^x=\left(\dfrac19\right)\\\\(3^1\cdot3^\frac12)^x=9^{-1}\\\\(3^{1+\frac12})^x=(3^2)^{-1}\\\\(3^{\frac32})^x=3^{-2}\\\\3^{\frac{3x}{2}}=3^{-2}\\\\\dfrac{3x}{2}=-2\\\\x=\dfrac{-4}{3}$