Answer:
The value of x is about 2.206.
Step-by-step explanation:
Consider the given equation is
[tex]2\ln x+\ln (x-2)=0[/tex]
We need to find the value of x.
Using the properties of logarithm we get
[tex]\ln x^2+\ln (x-2)=0[/tex] [tex][\because \ln a^b=b\ln a][/tex]
[tex]\ln (x^2(x-2))=0[/tex] [tex][\because \ln (ab)=\ln a+\ln b][/tex]
[tex]\ln (x^2(x-2))=ln 1[/tex] [tex][\because \ln 1=0][/tex]
On comparing both sides we get
[tex]x^2(x-2)=1[/tex]
[tex]x^3-2x^2=1[/tex]
Using graphing calculator, the real solution of the above equation is
[tex]x\approx 2.206[/tex]
Therefore, the value of x is about 2.206.
