Respuesta :

Answer:

x = [tex]\frac{1}{4}[/tex]

Step-by-step explanation:

Using the rules of logarithms

• log x + log y ⇔ log(xy)

• [tex]log_{b}[/tex] = n ⇔ x = [tex]b^{n}[/tex]

Given

ln 2x + ln 2 = 0

ln(2x × 2) = 0

ln 4x = 0

4x = [tex]e^{0}[/tex] = 1 ( divide both sides by 4 )

x = [tex]\frac{1}{4}[/tex]

Solving by property, In 2x + In 2 = 0 gives the value of x as 1/4 .

What are the properties of logarithm ?

The properties of logarithm are as follows -

  • lnx + lny = lnxy .
  • ln1 = 0 .

How to solve the given expression ?

The given expression is - In 2x + In 2 = 0

Using properties of logarithm to solve ,

⇒ ln(2x * 2) = 0

⇒ ln(4x) = ln1

Eliminating logarithm from both sides,

⇒ 4x = 1

∴  x = 1/4

Thus, solving by property, In 2x + In 2 = 0 gives the value of x as 1/4 .

To learn more about properties of logarithm, refer -

https://brainly.com/question/12049968

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