Respuesta :

Answer:

x = 10

Step-by-step explanation:

Using the rules of logarithms

• log x + log y ⇔ log(xy)

• log[tex]x^{n}[/tex] ⇔ n log x

• log x = log y ⇒ x = y

Given

ln20 + ln5 = 2 lnx , then

ln(20 × 5) = ln[tex]x^{2}[/tex]

ln 100 = ln[tex]x^{2}[/tex], hence

x² = 100 ( take the square root of both sides )

x = 10

The true solution is x = 10.

What is a Logarithm?

  • It is a mathematical function containing a base and an exponent, where the base is constant and the exponent can be variable or constant.
  • It is a non-linear function.

Given:

ln 20 + ln 5 = 2 ln x

We have to solve for x.

we know, by the property of logarithm.

⇒ ln A + ln B = ln (A×B)

⇒ n ln A = ln Aⁿ

⇒ If, ln A = ln B then A = B.

Now, we will solve for x.

⇒ ln 20 + ln 5 = 2 ln x  

⇒ ln (20 × 5) = ln x²

⇒ ln 100 = ln x²

⇒ x² = 100

Taking square root on both the sides, we get:

⇒ x = 10

Therefore, the true solution for the given equation is x = 10.

Learn more about the Logarithms here: https://brainly.com/question/14413095

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