Resposta:

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

Explicação passo a passo:

[tex]\sf{log_{\sqrt{8}}\:\sqrt{32} = log_{\sqrt{2^3}}\:\sqrt{2^5}}[/tex]

[tex]\sf{log_{\sqrt{8}}\:\sqrt{32} = log_{2^{\frac{3}{2}}}\:2^{\frac{5}{2}}}[/tex]

[tex]\sf{log_{\sqrt{8}}\:\sqrt{32} = \dfrac{5}{\not2}\:.\:\dfrac{\not2}{3}\:.\:log_2\:2}[/tex]

[tex]\sf{log_{\sqrt{8}}\:\sqrt{32} = \dfrac{5}{3}\:.\:1}[/tex]

[tex]\boxed{\boxed{\sf{log_{\sqrt{8}}\:\sqrt{32} = \dfrac{5}{3}}}}[/tex]