Solve for the exact value of x. 2ln(5x+5)+16=12 Answer:

Isolate logarithmic term: First, we need to isolate the logarithmic term by subtracting 16 from both sides of the equation. 2ln(5x+5) + 16 - 16 = 12 - 16 2ln(5x+5) = -4Divide by 2: Next, we divide both sides of the equation by 2 to solve for the natural logarithm of (5x+5). (2ln(5x+5))/2 = -4/2 ln(5x+5) = -2Exponentiate both sides: Now, we will exponentiate both sides of the equation to remove the natural logarithm. We use the property e^(ln(x)) = x. e^(ln(5x+5)) = e^(-2) 5x+5 = e^(-2)Subtract 5: We then subtract 5 from both sides to isolate the term with x. 5x + 5 - 5 = e^(-2) - 5 5x = e^(-2) - 5Divide by 5: Finally, we divide both sides by 5 to solve for x. 5x/5 = (e^(-2) - 5)/5 x = (e^(-2) - 5)/5

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Q. Solve for the exact value of

x

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2 \ln (5 x+5)+16=12

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Answer:

Isolate logarithmic term: First, we need to isolate the logarithmic term by subtracting $16$ from both sides of the equation. $\newline$ $2\ln(5x+5) + 16 - 16 = 12 - 16$ $\newline$ $2\ln(5x+5) = -4$
Divide by $2$ : Next, we divide both sides of the equation by $2$ to solve for the natural logarithm of $(5x+5)$ . $\frac{2\ln(5x+5)}{2} = \frac{-4}{2}$ $\ln(5x+5) = -2$
Exponentiate both sides: Now, we will exponentiate both sides of the equation to remove the natural logarithm. We use the property $e^{\ln(x)} = x$ . $\newline$ $e^{\ln(5x+5)} = e^{-2}$ $\newline$ $5x+5 = e^{-2}$
Subtract $5$ : We then subtract $5$ from both sides to isolate the term with $x$ . $\newline$ $5x + 5 - 5 = e^{-2} - 5$ $\newline$ $5x = e^{-2} - 5$
Divide by $5$ : Finally, we divide both sides by $5$ to solve for x. $\newline$ $\frac{5x}{5} = \frac{e^{(-2)} - 5}{5}$ $\newline$ $x = \frac{e^{(-2)} - 5}{5}$