Question

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

Answer 1

Ответ:

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

$x - 1 \leqslant 0 \\ 2x - 1 \leqslant 0$

$x \leqslant 1 \\ x \leqslant \frac{1}{2}$

$x\in<-\infty, 1]$

$lg(x - 1) - lg(2x - 1) = lg2.x\in < 1. + \infty >$

$lg( \frac{x - 1}{2x - 1} ) = lg2$

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

$\frac{x - 1}{2x - 1} = 2| \times 2x - 1$

$x - 1 = 2(2x - 1)$

$x - 1 = 4x - 2$

$x - 4x = - 2 + 1$

$1x - 4x = - 2 + 1$

$- 3x = - 1$

$- 3x = - 1| \div - 3$

$x = \frac{1}{3} .x \in < 1. + \infty >$

$Ø$