Solve for the exact value of x. 3ln(8x-8)+11=2 Answer:

Isolate natural logarithm term: Isolate the natural logarithm term. We start by subtracting 11 from both sides of the equation to isolate the term with the natural logarithm. 3ln(8x-8) + 11 - 11 = 2 - 11 3ln(8x-8) = -9Divide to solve logarithm: Divide both sides by 3 to solve for the natural logarithm of the expression. 3ln(8x-8) / 3 = -9 / 3 ln(8x-8) = -3Exponentiate to remove logarithm: Exponentiate both sides to remove the natural logarithm. e^(ln(8x-8)) = e^(-3) 8x - 8 = e^(-3)Add to solve for 8x: Add 8 to both sides to solve for 8x. 8x - 8 + 8 = e^(-3) + 8 8x = e^(-3) + 8Divide to solve for x: Divide both sides by 8 to solve for x. 8x / 8 = (e^(-3) + 8) / 8 x = (e^(-3) + 8) / 8

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Solve for the exact value of
x.

3ln(8x-8)+11=2
Answer:

Solve for the exact value of $x$ . $\newline$ $3 \ln (8 x-8)+11=2$ $\newline$ Answer:

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Q. Solve for the exact value of

x

\newline

3 \ln (8 x-8)+11=2

\newline

Answer:

Isolate natural logarithm term: Isolate the natural logarithm term. $\newline$ We start by subtracting $11$ from both sides of the equation to isolate the term with the natural logarithm. $\newline$ $3\ln(8x-8) + 11 - 11 = 2 - 11$ $\newline$ $3\ln(8x-8) = -9$
Divide to solve logarithm: Divide both sides by $3$ to solve for the natural logarithm of the expression. $\frac{3\ln(8x-8)}{3} = \frac{-9}{3}$ $\ln(8x-8) = -3$
Exponentiate to remove logarithm: Exponentiate both sides to remove the natural logarithm. $\newline$ $e^{\ln(8x-8)} = e^{-3}$ $\newline$ $8x - 8 = e^{-3}$
Add to solve for $8x$ : Add $8$ to both sides to solve for $8x$ . $\newline$ $8x - 8 + 8 = e^{-3} + 8$ $\newline$ $8x = e^{-3} + 8$
Divide to solve for x: Divide both sides by $8$ to solve for $x$ . $\newline$ $\frac{8x}{8} = \frac{e^{(-3)} + 8}{8}$ $\newline$ $x = \frac{e^{(-3)} + 8}{8}$