Resposta:
[tex]\displaystyle log_3\frac{81\sqrt{3}}{\sqrt[3]{3}} =\frac{25}{6}[/tex]
Explicação passo-a-passo:
[tex]\displaystyle log_3\frac{81\sqrt{3}}{\sqrt[3]{3}} =log_3\frac{3^4.3^{\frac{^1}{2}} }{3^{\frac{1}{3}}} =log_33^4.3^{\frac{1}{2}}.3^{-\frac{1}{3}}=log_33^{(4+\frac{1}{2}-\frac{1}{3})}=log_33^{\frac{(24+3-2)}{6}}=\\\\\\log_33^{\frac{25}{6} }=x\\\\3^x=3^{\frac{25}{6}}\\\\x=\frac{25}{6}[/tex]
