Question

Решите неравенство
1) lg(3x−17)=lg(x+1)
2) log2 (x - 1) - log2 (2x - 4) = 0
3)log2 (2x ² + 7) = log2 (x ² + 8)
4)log2 (x² + 3) = log2 (2x ² + x + 1)
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Answer 1

Explicație pas cu pas:

$3x - 17 > 0;x + 1 > 0 = > x > \frac{17}{3} \\ 3x - 17 = x + 1 \\ 3x - x = 1 + 17\\ 2x = 18 = > x = 9$

$x - 1 > 0;2x - 4 > 0 = > x > 2 \\ x - 1 = 2x - 4 \\ x - 2x = - 4 + 1 \\ - x = - 3 = > x = 3$

$2x ² + 7 > 0;x ² + 8 > 0 = > x \: real\\ 2x ² + 7 = x ² + 8 \\ 2 {x}^{2} - {x}^{2} = 8 - 7 \\ {x}^{2} = 1 \\ x = - 1;x = 1$

$x² + 3 > 0; 2x ² + x + 1 > 0 = > x \: real \\ x² + 3 = 2x ² + x + 1 \\ x² + 3- 2x ² - x - 1 = 0 \\ - {x}^{2} - x + 2 = 0 \\ {x}^{2} + x - 2 = 0 \\ (x + 2)(x - 1) = 0 \\ x = - 2;x = 1$