Log2 (2sin^2 2x + 1) - 2log2 cos x = 1 + log2 5

Lg2 (2sin^2 2x+1) - log2 cos^2x=lg2 2+lg2 5

(2sin^2 2x+1) / cos^2x=10

2*4sin^2xcos^2x+1=10cos^2x

8cos^2x (1-cos^2x) + 1=10cos^2x

8cos^2x-8cos^4x+1=10cos^2x

cos^2x=t t>0

8t^2+2t-1=0

t = (-1+-3) / 8

t1=1/4 t2=-1/2

cosx=1/2 cos=-1/2

x=+-п/3+2 пk

x=П+-П/3+2 Пk