(X+1)^(lg(x+1))=100(x+1)

lg((x+1)^(lg(x+1))) = lg(100(x+1))
lg(x+1)*lg(x+1)=lg100+lg(x+1)
lg^2(x+1) - lg(x+1) - 2=0
lg(x+1)= a
a^2 - a - 2=0
D = 9
a1 = - 1
a2 = 2

lg(x+1) = - 1    x+1>0
x+1 = 1/10       x> - 1
x = - 9/10

lg(x+1) = 2    x> - 1
x+1 = 100
x = 99

Ответ:  - 9/10,  99