Question

Log5(7x+4)-log5(2x-1)=1

Answer 1

Ответ:

Объяснение:

log5(7x + 4) - log5(2x - 1) = 1

   ОДЗ: 7x + 4 ≤ 0 и 2x - 1 ≤ 0

              x ≤ - $\frac{4}{7}$           x ≤ $\frac{1}{2}$

              x ∈ ( - ∞; $\frac{1}{2}$ ] ===≥  x ∈ ($\frac{1}{2}$ ; + ∞)

log5(7x + 4) - log5(2x - 1) = 1

log5($\frac{7x + 4}{2x -1}$) = 1

$\frac{7x +4}{2x - 1}$ = $5^{1}$

$\frac{7x + 4}{2x - 1}$ = 5

7x + 4 = 5(2x - 1)

7x + 4 = 10x - 5

7x - 10[ =  - 5 - 4

- 3x = - 9

x = 3

x ∈ ($\frac{1}{2}$ ; + ∞)

x = 3