The value of x is:
[tex]x=13[/tex]
We are asked to solve the equation:
[tex]2\ln 3=\ln (x-4)[/tex]
i.e. we are asked to find the value of x which satisfies the equation.
We know that:
[tex]a\ln b=\ln b^a[/tex]
i.e.
[tex]2\ln 3=\ln 3^2\\\\i.e.\\\\2\ln 3=\ln 9[/tex]
i.e. the equation is written as:
[tex]\ln 9=\ln (x-4)[/tex]
Now on taking exponential on both the side of the equation we get:
[tex]e^{\ln 9}=e^{\ln (x-4)}\\\\i.e.\\\\9=x-4[/tex]
since,
[tex]e^{\ln x}=x[/tex]
Hence, we get:
[tex]x=9+4\\\\i.e.\\\\x=13[/tex]
The answer is: [tex]x=13[/tex]
