15 ? ?

2(7)^(3x+1) = 48

solve for x.

(using ln)

a) 0.411
b) 0.311
c) 0.011
d) 0.211
e) 0.111

The answer is:  [D]:  0.211 .

Explanation:

Given:  2(7)^(3x+1) = 48; Solve for "x" (using "ln");

First, divide EACH side of the equation by: "2" ;

 → [2(7)^(3x+1)] / 2 = 48 / 2 ;

to get:  → 7^(3x+1) = 24 ;

→ Now, take the "ln" of EACH side of the equation:

→  ln [7^(3x+1)] = ln 24 ; 

→ (3x+1) ln 7 = ln 24 ; 

→  Divide EACH side of the equation by "ln 7" ; 

→  [(3x+1) (ln 7)] / ln 7 = (ln 24 / ln 7) ;

→ 3x + 1 = (ln 24 /ln 7)

               (Using calculator, "(ln 24 / ln 7)" equals: "1.63319659538");

→ 3x + 1 = 1.63319659538 ; 

→ Subtract "1" from EACH side of the equation; 

→ 3x + 1 − 1 = 1.63319659538 − 1 ; 

→ 3x = 0.63319659538 ; 

→ Now, divide EACH side of the equation by "3"; to isolate "x" on one side of the equation; and to solve for "x" ; 

→ 3x / 3 = 0.63319659538 / 3 ;  (using calculator); 

to get: 

→ x = 0.2110655317933333  ; which is: 
  Answer choice: [D]: 0.211  (rounded).