Lg (cos^2014 x) = lg (sin^2014 x)

cos^2 (2014x) = sin^2 (2014 x) ;

cos^2 (2014x) - sin^2 (2014x) = 0;

(cos (2014x) - sin (2014x) * (cos (2014x) + sin (2014x)) = 0;

1) cos (2014x) = sin (2014x) ; / cos (2014x) ≠ 0;

tg (2014x) = 1;

2014 x = pi/4 + pi*k;

x = pi/8416 + pik / 2014; k ∈ Z.

2) cos (2014x) = - sin (2014x) ; / cos (2014x) ≠ 0;

tg (2014 x) = - 1;

x = - pi/4 + pi*k;

x = - pi/8416 + pi/2014; k∈Z.

Объединив 2 ответа, получим

x = + - pi/8416 + pi*k / 2014; k ∈ Z