Question

Решите показательное уравнение 0.2^1-x - 0.2^3-x=120

Answer 1

${0.2}^{1} \times {0.2}^{ - x} - {0.2}^{3} \times {0.2}^{ - x} = 120 \\ {0.2}^{ - x} - {0.2}^{2} \times 0.2 {}^{ - x} = 600 \\ t - 0.04t = 600 \\ 0.96t = 600 \\ t = 625 \\ {0.2}^{ - x} = 625 \\ \frac{1}{5} {}^{ - x} = 625 \\ x = 4$

Ответ: 4.