The domain of the function `f(x) = log_(3/2) log_(1/2)log_pi log_(pi/4) x` is

Options

A. `(0, oo)`
B. `(0, ((pi)/(4))^(pi))`
C. `(((pi)/(2))^(pi), (pi)/(4))`
D. `(((pi)/(2))^(pi), oo)`

Answer

C

Explanation

`f(x) =log_((3)/(2)) log_((1)/(2)) log_(pi) log_((pi)/(4)) x`
For f(x) to be real
`log_((1)/(2)) log_(pi) log_((pi)/(4)) x gt 0`
`rArr 0 lt log_(pi) log_((pi)/(4)) x lt ((1)/(2))^(@) =1 rArr ((pi)/(4))^(pi) lt x lt (pi)/(4)`
`rArr pi^(@) lt log_((pi)/(4)) x lt pi rArr x in (((pi)/(4))^(pi), (pi)/(4))`