Question

Se LOGX 4= -1/2 e LOG32 Y = 1/5, então (Y+1)/X


EXATAMENTE ASSIM MAS N CONSEGUI 

Answer 1

Bom, exercício com aplicação das propriedades de log.

Primeiramente, vamos encontrar o X e o Y.

$Log\ _4\ x = -\frac{1}{2}\\\\ 4^-^ \frac{1}{2} = x\\\\ 4 = 2^2\\\\\ x = 2^-^ \frac{2}{2}\\\\ x = 2^-^1\\\\\ \boxed{x = \frac{1}{2}}$

Agora o Y.

$Log\ _3_2\ Y = \frac{1}{5}\\\\\ Y = 32^ \frac{1}{5}\\\\ 32 = 2^5\\\\\ Y = 2^ \frac{5}{5}\\\\\ Y=2^1\\\\\ \boxed{Y=2}$

Agora, resolvemos o que se pede:

$\frac{(y+1)}{x} = \frac{(2+1)}{\frac{1}{2}} = \frac{3}{\frac{1}{2}} = 6\\\\\ \boxed{\boxed{6}}$