Question

Solve: 2 In 3 = In(x-4)
X=9
X=10
X=13

Answer 1

x = 13

Explanation:

`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`

Answer 2

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

_________________________________________

Explanation:

_________________________________________

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 ;

_____________________________________

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

_____________________________________