Question

Решение логарифмических уравнений.

Answer 1

1.

lg(x-1)-lg(2x-11)=lg2

$\displaystyle \: lg( \frac{x - 1}{2x - 11} ) = lg(2)$

$\displaystyle\frac{x - 1}{2x - 11} = 2$

$x - 1 = 4x - 22$

$x = 7$

Ответ:7

2.

lg(3x-1)-lg(x+5)=lg5

$\displaystyle \: lg( \frac{3x - 1}{x + 5} ) = lg(5)$

$\displaystyle\frac{3x - 1}{x + 5} = 5$

$3x - 1 = 5x + 25$

$x = - 13$

Ответ:-13

3.

$log_{3}( {x}^{3} - x) - log_{3}(x) = log_{3}(3)$

$\displaystyle log_{3}( \frac{ {x}^{3} - x}{x} ) = log_{3}(3)$

$\displaystyle \frac{ {x}^{3} - x }{x} = 3$

${x}^{3} - x = 3x$

${x}^{3} - x - 3x = 0$

$x( {x}^{2} - 1 - 3) = 0 \\ x( {x}^{2} - 4) = 0$

x=0

x=±2

Ответ:2