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Solve for the exact value of
x.

2ln(2x-4)+6=16
Answer:

Solve for the exact value of $x$ . $\newline$ $2 \ln (2 x-4)+6=16$ $\newline$ Answer:

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Full solution

Q. Solve for the exact value of

x

.

\newline

2 \ln (2 x-4)+6=16

\newline

Answer:

Isolate Logarithmic Expression: Isolate the logarithmic expression by subtracting $6$ from both sides of the equation. $\newline$ $2\ln(2x-4) + 6 - 6 = 16 - 6$ $\newline$ $2\ln(2x-4) = 10$
Divide to Solve Natural Logarithm: Divide both sides of the equation by $2$ to solve for the natural logarithm of $(2x-4)$ . $\newline$ $\frac{2\ln(2x-4)}{2} = \frac{10}{2}$ $\newline$ $\ln(2x-4) = 5$
Exponentiate to Remove Logarithm: Exponentiate both sides of the equation to remove the natural logarithm, using the property $e^{\ln(x)} = x$ . $\newline$ $e^{\ln(2x-4)} = e^5$ $\newline$ $2x - 4 = e^5$
Add to Isolate Term: Add $4$ to both sides of the equation to isolate the term with $x$ . $\newline$ $2x - 4 + 4 = e^5 + 4$ $\newline$ $2x = e^5 + 4$
Divide to Solve for x: Divide both sides of the equation by $2$ to solve for x. $\newline$ $\frac{2x}{2} = \frac{e^5 + 4}{2}$ $\newline$ $x = \frac{e^5 + 4}{2}$

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