Bom, exercício com aplicação das propriedades de log.
Primeiramente, vamos encontrar o X e o Y.
[tex]Log\ _4\ x = -\frac{1}{2}\\\\ 4^-^ \frac{1}{2} = x\\\\ 4 = 2^2\\\\\ x = 2^-^ \frac{2}{2}\\\\ x = 2^-^1\\\\\ \boxed{x = \frac{1}{2}}[/tex]
Agora o Y.
[tex]Log\ _3_2\ Y = \frac{1}{5}\\\\\ Y = 32^ \frac{1}{5}\\\\ 32 = 2^5\\\\\ Y = 2^ \frac{5}{5}\\\\\ Y=2^1\\\\\ \boxed{Y=2}[/tex]
Agora, resolvemos o que se pede:
[tex]\frac{(y+1)}{x} = \frac{(2+1)}{\frac{1}{2}} = \frac{3}{\frac{1}{2}} = 6\\\\\ \boxed{\boxed{6}}[/tex]
