Resposta:

[tex]\textsf{Leia abaixo}[/tex]

Explicação passo a passo:

[tex]\sf log_{\sqrt[\sf 3]{\sf 4}}\:2 = log_{\sqrt[\sf 3]{\sf 2^2}}\:2[/tex]

[tex]\sf log_{\sqrt[\sf 3]{\sf 4}}\:2 = log_{2^{\frac{2}{3}}}\:2[/tex]

[tex]\sf log_{\sqrt[\sf 3]{\sf 4}}\:2 = \dfrac{3}{2}\:.\:log_{2}\:2[/tex]

[tex]\sf log_{\sqrt[\sf 3]{\sf 4}}\:2 = \dfrac{3}{2}\:.\:1[/tex]

[tex]\boxed{\boxed{\sf log_{\sqrt[\sf 3]{\sf 4}}\:2 = \dfrac{3}{2}}}[/tex]