Solve for the exact value of x. 6ln(3x+2)+20=56 Answer:

Isolate natural logarithm term: First, we need to isolate the natural logarithm term on one side of the equation. 6ln(3x+2) + 20 = 56 Subtract 20 from both sides to get: 6ln(3x+2) = 56 - 20 6ln(3x+2) = 36Divide by 6: Now, divide both sides by 6 to solve for the ln(3x+2) term. (6ln(3x+2)) / 6 = 36 / 6 ln(3x+2) = 6Exponentiate using base e: To remove the natural logarithm, we will exponentiate both sides using the base e. e^(ln(3x+2)) = e^6 Since e^(ln(a)) = a, we have: 3x + 2 = e^6Subtract 2: Subtract 2 from both sides to isolate the term with x. 3x + 2 - 2 = e^6 - 2 3x = e^6 - 2Divide by 3: Finally, divide both sides by 3 to solve for x. 3x / 3 = (e^6 - 2) / 3 x = (e^6 - 2) / 3

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Solve for the exact value of
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6ln(3x+2)+20=56
Answer:

Solve for the exact value of $x$ . $\newline$ $6 \ln (3 x+2)+20=56$ $\newline$ Answer:

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Q. Solve for the exact value of

x

\newline

6 \ln (3 x+2)+20=56

\newline

Answer:

Isolate natural logarithm term: First, we need to isolate the natural logarithm term on one side of the equation. $\newline$ $6\ln(3x+2) + 20 = 56$ $\newline$ Subtract $20$ from both sides to get: $\newline$ $6\ln(3x+2) = 56 - 20$ $\newline$ $6\ln(3x+2) = 36$
Divide by $6$ : Now, divide both sides by $6$ to solve for the $\ln(3x+2)$ term. $\newline$ $(6\ln(3x+2)) / 6 = 36 / 6$ $\newline$ $\ln(3x+2) = 6$
Exponentiate using base $e$ : To remove the natural logarithm, we will exponentiate both sides using the base $e$ . $\newline$ $e^{\ln(3x+2)} = e^6$ $\newline$ Since $e^{\ln(a)} = a$ , we have: $\newline$ $3x + 2 = e^6$
Subtract $2$ : Subtract $2$ from both sides to isolate the term with $x$ . $\newline$ $3x + 2 - 2 = e^{6} - 2$ $\newline$ $3x = e^{6} - 2$
Divide by $3$ : Finally, divide both sides by $3$ to solve for x. $\newline$ $\frac{3x}{3} = \frac{e^6 - 2}{3}$ $\newline$ $x = \frac{e^6 - 2}{3}$