Question

Решите логарифмические уравнение

Answer 1

Ответ:

2.

$lg(x) = 3 \\ x = {10}^{3} \\ x = 1000$

3.

$log_{x}(8) = 3 \\ {x}^{3} = 8 \\ x = 2$

4.

$- 2 log_{2} {}^{2} (x) - 5 log_{2}(x) + 3 = 0 \\ \\ log_{2}(x) = t \\ \\ - 2t {}^{2} - 5t + 3 = 0 \\ 2t {}^{2} + 5t - 3 = 0\\ D = 25 + 24 = 49 \\ t_1 = \frac{ - 5 + 7}{4} = \frac{1}{2} \\ t_2 = - 3 \\ \\ log_{2}(x) = \frac{1}{2} \\ x_1 = \sqrt{2} \\ \\ log_{2}(x) = - 3 \\ x_2 = {2}^{ - 3} = \frac{1}{8}$

5.

$log_{2}(x) \geqslant 4 \\ x \geqslant {2}^{4} \\ x \geqslant 16 \\ \\ \text{ОДЗ:} \\ x > 0 \\ \\ \text{Ответ:} \\ x\in[16 ;+ \infty )$

6.

$lg(x + 3) < 1 \\ x + 3 < 10 \\ x < 7 \\ \\ \text{ОДЗ:} \\ x + 3 > 0 \\ x > - 3 \\ \\ \text{Ответ:} \\ x\in( - 3;7)$