Question

Boa Noite! Ajudem-me please!

log $3/3 \sqrt{} 3$ na base $\sqrt[4]{3}$

Answer 1

  3.3^-1/3 = (3^1/4)^x
   
     3^(1-1/3) =  3^x/4
     3^(2/3) =  3^x/4
           2  =  x
           3      4
   3x = 8

  x =  8
         3

Answer 2

$log_ \sqrt[4]{3}\ \frac{3}{ \sqrt[3]{3}} } = x\\\\ (\sqrt[4]{3})^x=\frac{3}{ \sqrt[3]{3}} }\\\\ (\sqrt[4]{3})^x=\frac{3^1}{3^\frac{1}{3}}\\\\ (\sqrt[4]{3})^x = 3^1^-^\frac{1}{3}\\\\ 3^\frac{1x}{4} = 3^\frac{2}{3}\\\\ \frac{x}{4}=\frac{2}{3}\\\\ \boxed{x=\frac{8}{3}}$