The answer is: [D]: 0.211 .
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Explanation:
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Given: 2(7)^(3x+1) = 48; Solve for "x" (using "ln");
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First, divide EACH side of the equation by: "2" ;
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→ [2(7)^(3x+1)] / 2 = 48 / 2 ;
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to get: → 7^(3x+1) = 24 ;
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→ Now, take the "ln" of EACH side of the equation:
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→ 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)
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(Using calculator, "(ln 24 / ln 7)" equals: "1.63319659538");
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→ 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" ;
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→ 3x / 3 = 0.63319659538 / 3 ; (using calculator);
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to get:
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→ x = 0.2110655317933333 ; which is:
Answer choice: [D]: 0.211 (rounded).
