Question

cos($frac{ pi }{2} +x)=1$
$log_{5} (5-x)= log_{5} 3$
$sqrt{2} cosx-1=0$

Answer 1

cos(π/2+x) = 1
  π/2 + x = 2πk  ;  k∈Z
x= 2πk - π/2 = (4k-1)·π/2  ;  k∈Z

log(5) (5-x) - log(5) 3 = 0
log(5) [(5-x)/3] = 0
  (5-x)/3 = 1
   5-x = 3
    x=2

cosx = 1/√2 = √2/2
    x = +/-π/4 + 2πk  ;  k∈Z