Question

Log0. 5*(3x+4)=log0.5*(2x-2)

Answer 1

Ответ:

$log_{0.5}(3x + 4) = log_{0.5}(2x - 2) \\ \\ odz \\ 3x + 4 > 0 \\ 2x - 2 > 0 \\ \\ x > - \frac{4}{3} \\ x > 1 \\ \\ = > x > 1$

$3x + 4 = 2x - 2 \\ x = - 6$

в одз не входит, корней нет.

Ответ: нет корней

Answer 2

To solve the equation $\log_{0.5}(3x+4) = \log_{0.5}(2x-2)$, you can use the properties of logarithms.

1. First, notice that both sides have the same base of $0.5$. Therefore, you can equate the expressions inside the logarithms:

$$3x + 4 = 2x - 2$$

2. Now, solve for $x$:

$$3x - 2x = -2 - 4$$

$$x = -6$$

So, the solution to the equation is $x = -6$.