Question

Como resolvo Log 3 na base 3√3?

Answer 1

$x=\mathrm{\ell og}_{3\sqrt{3}}\left(3 \right )\\ \\ \left(3\sqrt{3} \right )^{x}=3\\ \\ \left(3 \cdot 3^{\,^{1}\!\!\!\diagup\!\!_{2}} \right )^{x}=3^{1}\\ \\ \left(3^{1+\,^{1}\!\!\!\diagup\!\!_{2}} \right )^{x}=3^{1}\\ \\ \left(3^{\,^{\left(2+1 \right )}\!\!\!\diagup\!\!_{2}} \right )^{x}=3^{1}\\ \\ \left(3^{\,^{3}\!\!\!\diagup\!\!_{2}} \right )^{x}=3^{1}\\ \\ 3^{\,^{3x}\!\!\!\diagup\!\!_{2}}=3^{1}\\ \\ \\ \dfrac{3x}{2}=1\\ \\ 3x=2\\ \\ x=\dfrac{2}{3} \;\;\Rightarrow\;\;\boxed{\mathrm{\ell og}_{3\sqrt{3}}\left(3 \right )=\dfrac{2}{3}}$