lg(x^(lgx)) = lg(100x^2)
кстати ОДХ x > 0
lgx*lgx = lg100 + 2lgx
lg^2x = 2 + 2lgx
Сделаем замену lgx = t
t^2 - 2t - 2 = 0
t1 = 1-sqrt(3)
t2 = 1+sqrt(3)
lgx=1-sqrt(3)
x = 10^(1-sqrt(3))
lgx = 1+sqrt(3)
x = 10^(1+sqrt(3))
[b]Ответ: [/b]10^(1-sqrt(3)) и 10^(1+sqrt(3))