Помогите решить. lg lg(x-1)=lg lg (2x+1)-lg2

Решение:
lg [lg(x-1)] = lg [lg (2x+1)] - lg2
lg [lg(x-1)] = lg [lg (2x+1)]/2
lg(x-1) = [lg (2x+1)] /2
ОДЗ: х-1>0 => x>1
2lg(x-1) = lg (2x+1)
lg (x-1)^2 = lg (2x+1)
(x-1)^2 = 2x+1
x^2 - 2x + 1 = 2x + 1
x^2 - 4x = 0
x(x-4) = 0
x = 0 - не подходит по ОДЗ.
x-4 = 0 => x=4
Ответ: х=4
Проверка:
х=4
lg [lg(x-1)] = lg [lg (2x+1)] - lg2
lg [lg(4-1)] = lg [lg (2*4+1)] - lg2
lg [ lg 3] = lg [lg 9] - lg 2
lg [lg 9] - lg [ lg 3] = lg 2
lg [lg 9] - lg [ lg 3] = lg [lg 9/lg 3] = lg [log 3(9)] = lg 2