Question

㏒$_{9}$ (3√3)

Log$_{2}$ $^{8} \sqrt{64}$

Answer 1

Primeiro exercício

log_{9}(3√3)

$\ell og_{9}(3\sqrt{3})\\\\\ell og_{3^2}(3\sqrt{3})\\\\\frac{1}{2}\cdot \ell og_3(3\sqrt{3})\\\\\frac{1}{2}\cdot\begin{pmatrix}\ell og_{3}(3)+\ell og_{3}( \sqrt{3} )\end{pmatrix}\\\\\frac{1}{2}\cdot\begin{pmatrix}1+\ell og_{3}(3^{\frac{1}{2}})\end{pmatrix}\\\\\frac{1}{2}\cdot\begin{pmatrix}1+ \frac{1}{2}\cdot \ell og_{3}(3)\end{pmatrix}\\\\\frac{1}{2}\cdot\begin{pmatrix}1+ \frac{1}{2}\cdot 1\end{pmatrix}\\\\ \frac{1}{2} \cdot \begin{pmatrix}1+ \frac{1}{2}\end{pmatrix}$

$\frac{1}{2}\cdot\begin{pmatrix}\frac{2}{2}+\frac{1}{2}\end{pmatrix}\\\\\frac{1}{2}\cdot(\frac{3}{2})\\\\\frac{3}{4}$

Segundo exercício
 
log_{2}(⁸√64)

$\ell og_{2}(\sqrt[8]{64})\\\\\ell og_{2}(\sqrt[8]{2^6})\\\\\ell og_{2}(2^{\frac{6}{8}})\\\\\frac{6}{8}\cdot \ell og_{2}(2)\\\\\frac{6}{8}\cdot 1\\\\\frac{6}{8}\\\\\frac{6\div 2}{8\div 2}~~(simplifica\c{c}\~ao)\\\\\frac{3}{4}$