Question

Log 1/2( 2x - 3,5)< 1

Answer 1

$log_{\frac{1}{2} }( 2x - 3,5)< 1$

ОДЗ:

$2x-3,5>0$

$2x>3,5$

$x>1,75$

$log_{\frac{1}{2} }( 2x - 3,5)< log_{\frac{1}{2}}0,5$

$2x - 3,5>0,5$

$2x >0,5+3,5$

$2x >4$

$x>2$

Ответ: $(2;+$ ∞ $)$

Answer 2

To solve the inequality log₁/₂(2x - 3.5) < 1, we can rewrite it in exponential form:

1/₂^(log₁/₂(2x - 3.5)) < 1

Now, let's simplify the inequality:

(2x - 3.5) < 2

Next, solve the inequality for x:

2x - 3.5 < 2

Add 3.5 to both sides:

2x < 5.5

Divide both sides by 2:

x < 5.5/2

x < 2.75

Therefore, the solution to the inequality log₁/₂(2x - 3.5) < 1 is x < 2.75.