31. xlgx = 100x

Решим уравнение x^lgx = 100x

lg(x^lgx) = lg(100x)

lgx * lgx = lg100 + lgx

(lgx)² = 2 + lgx

(lgx)² - lgx - 2 = 0

Пусть y = lgx

y² - y - 2 = 0

D = 1 + 8 = 9

y = (1 +- 3)/2

y = 2 или y = -1

lgx = 2 или lgx = -1

x = 10² = 100 или x = 10^-1 = 0.1

Ответ: 0.1, 100