1 Answer

Kasun Gajasinghe · Answer 1 · 2022-01-04T03:42:47+0000

Answer:

The value of x is about 2.206.

Explanation:

Consider the given equation is

$2\ln x+\ln (x-2)=0$

We need to find the value of x.

Using the properties of logarithm we get

$\ln x^2+\ln (x-2)=0$
$[\because \ln a^b=b\ln a]$

$\ln (x^2(x-2))=0$
$[\because \ln (ab)=\ln a+\ln b]$

$\ln (x^2(x-2))=ln 1$
$[\because \ln 1=0]$

On comparing both sides we get

x^2(x-2)=1

x^3-2x^2=1

Using graphing calculator, the real solution of the above equation is

$x\approx 2.206$

Therefore, the value of x is about 2.206.

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