Question

Log 0,5(2x-6)>log0,5(2)​

Answer 1

Ответ:

log₀,₅(2x+6)-log₀,₅4>0 ОДЗ: 2x+6>0 2x>-6 x>-3 ⇒ x∈(-3;+∞)

log₀,₅(2x+6)>log₀,₅4

2x+6<4

2x<-2

x<-1 ⇒

Ответ: x∈(-3;-1).

Answer 2

Ответ:

logo,5(2x+6)-logo,54>0

ОДЗ: 2х+6>0

2x>-6

x>-3 = XE(-3;too)

logo,5(2x+6)>log0,54

2x+6<4 2x<-2

X<-1 →

Ответ: x€(-3;-1).

Answer 3

To solve the inequality log₀.₅(2x-6) > log₀.₅(2), you can use the properties of logarithms. In this case, since both sides of the inequality have the same base (0.5), you can set the expressions inside the logarithms equal to each other and solve for x:

log₀.₅(2x-6) = log₀.₅(2)

Now, you can remove the logarithms by raising both sides to the power of 0.5 (since log base 0.5 and 0.5 as an exponent cancel each other out):

2x - 6 = 2

Now, isolate x by adding 6 to both sides:

2x = 2 + 6 2x = 8

Divide both sides by 2 to solve for x:

x = 8 / 2 x = 4

So, the solution to the inequality log₀.₅(2x-6) > log₀.₅(2) is x > 4.