Respuesta :

JonHenderson55

Answer:  The correct answer is:  [D]:  " x = 13 " .

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Step-by-step explanation:

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Given:  

 2 ln 3 = ln (x - 4) ;  Solve for x  ;

Note:  2 ln 3 = ln 3² = ln (3 * 3) = ln 9 ;

  ln 9 = ln (x -4) ;

      9 = x - 4 ;

Add "4"  to each side of the equation;  

 to isolate "x" on one side of the equation;

      & to solve for "x" ;

   

      9 + 4 = x - 4 + 4 ;

to get:

        13 = x ;

↔  x = 13 ;

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    →  which is:  Answer choice:  [D]:  " x = 13 " .

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gmany

Answer:

x = 13

Step-by-step explanation:

[tex]2\ln3=\ln(x-4)\\\\\text{Domain:}\\\\x-4>0\qquad\text{add 4 to both sides}\\x-4+4>0+4\\\boxed{x>4}\\====================\\\text{use}\ \log_ab^n=n\log_ab\\\\\ln3^2=\ln(x-4)\iff3^2=x-4\qquad\text{add 4 to both sides}\\\\9+4=x-4+4\\\\13=x\to x=13\in D[/tex]

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