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Solve for the exact value of
x.

2ln(2x-2)+12=8
Answer:

Solve for the exact value of $x$ . $\newline$ $2 \ln (2 x-2)+12=8$ $\newline$ Answer:

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Find trigonometric ratios using a Pythagorean or reciprocal identity

Full solution

Q. Solve for the exact value of

x

.

\newline

2 \ln (2 x-2)+12=8

\newline

Answer:

Isolate logarithmic expression: Isolate the logarithmic expression. $\newline$ We start by subtracting $12$ from both sides of the equation to isolate the logarithmic term. $\newline$ $2\ln(2x-2) + 12 - 12 = 8 - 12$ $\newline$ $2\ln(2x-2) = -4$
Divide to solve ln term: Divide both sides by $2$ to solve for the ln term. $\newline$ Divide both sides by $2$ to isolate $\ln(2x-2)$ . $\newline$ $(2\ln(2x-2)) / 2 = -4 / 2$ $\newline$ $\ln(2x-2) = -2$
Exponentiate to remove ln: Exponentiate both sides to remove the natural logarithm. $\newline$ We raise $e$ to the power of both sides of the equation to remove the natural logarithm. $\newline$ $e^{\ln(2x-2)} = e^{-2}$ $\newline$ $2x - 2 = e^{-2}$
Add to solve for $2x$ : Add $2$ to both sides to solve for $2x$ . $\newline$ Add $2$ to both sides of the equation to isolate the term with $x$ . $\newline$ $2x - 2 + 2 = e^{(-2)} + 2$ $\newline$ $2x = e^{(-2)} + 2$
Divide to solve for x: Divide both sides by $2$ to solve for $x$ . $\newline$ Divide both sides by $2$ to find the value of $x$ . $\newline$ $\frac{2x}{2} = \frac{e^{(-2)} + 2}{2}$ $\newline$ $x = \frac{e^{(-2)} + 2}{2}$

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