Решить уравнение: (x-1)lg2=1-lg(1+2 в степени x)

(x - 1) * lg 2 = 1 - lg (1 + 2 ^ x);
(x - 1) * lg 2 = lg 10 - lg (1 + 2 ^ x);
(x - 1) * lg 2 = lg (10/(1 + 2 ^ x));
lg 2 ^ (x - 1) = lg (10/(1 + 2 ^ x));
2 ^ (x - 1) = 10/(1 + 2 ^ x);
2 ^ (x - 1) * (1 + 2 ^ x) = 10;
2 ^ x * 1/2 * (1 + 2 ^ x) = 10;
2 ^ x * (1 + 2 ^ x) = 20;
2 ^ x * (1 + 2 ^ x) - 20 = 0;
(2 ^ x) ^ 2 + 2 ^ x - 20 = 0;
D = 1 - 4 * 1 * (- 20) = 81;
1) 2 ^ x = (- 1 + 9)/2;
2 ^ x = (8)/2;
2 ^ x = 4;
x = 2;
2) 2 ^ x = (- 1 - 9)/2;
2 ^ x = - 5;
x = log2 (-5);
Ответ: x = 2 и x = log2 (-5).