Question

Решите уровнение log0. 2(2x-4)=-1

Answer 1

Ответ: x=4,5.

Объяснение:

log₀,₂(2x-4)=-1    ОДЗ: 2x-4>0   2x>4  |÷2    x>2  ⇒   x∈(2;+∞).

2x-4=0,2⁻¹

2x-4=(1/5)⁻¹

2x-4=5

2x=9  |÷2

x=4,5 ∈ОДЗ.

Answer 2

To solve the equation log₀.₂(2x - 4) = -1, we need to use the properties of logarithms. The base of the logarithm is 0.2, which is the same as 1/5.

Step 1: Rewrite the equation using the definition of logarithms. log₀.₂(2x - 4) = -1 is equivalent to 0.2⁻¹ = 2x - 4.

Step 2: Simplify the left-hand side of the equation. 0.2⁻¹ is the same as 5, so we have 5 = 2x - 4.

Step 3: Isolate the variable x on one side of the equation. Add 4 to both sides to get rid of the -4 on the right side. 5 + 4 = 2x.

Step 4: Simplify further. 9 = 2x.

Step 5: Solve for x by dividing both sides by 2. x = 9 / 2.

So the solution to the equation is x = 4.5.