Solve for the exact value of x. 3ln(2x+7)+14=20 Answer:

Isolate natural logarithm term: First, we need to isolate the natural logarithm term by subtracting 14 from both sides of the equation. 3ln(2x+7) + 14 - 14 = 20 - 14Simplify by subtraction: Now, we simplify the equation by performing the subtraction. 3ln(2x+7) = 6Divide to isolate logarithm: Next, we divide both sides of the equation by 3 to isolate the natural logarithm. (3ln(2x+7))/3 = 6/3Get logarithm by itself: After dividing, we get the natural logarithm by itself. ln(2x+7) = 2Exponentiate using base e: To eliminate the natural logarithm, we will exponentiate both sides of the equation using the base e. e^(ln(2x+7)) = e^2Simplify left side: Since e^(ln(x)) = x for any x, we can simplify the left side of the equation. 2x+7 = e^2Isolate term with x: Now, we subtract 7 from both sides to isolate the term with x. 2x + 7 - 7 = e^2 - 7Simplify by subtraction: Simplify the equation by performing the subtraction. 2x = e^2 - 7Divide to solve for x: Finally, we divide both sides by 2 to solve for x. 2x/2 = (e^2 - 7)/2Get exact value of x: After dividing, we get the exact value of x. x = (e^2 - 7)/2

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Solve for the exact value of
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3ln(2x+7)+14=20
Answer:

Solve for the exact value of $x$ . $\newline$ $3 \ln (2 x+7)+14=20$ $\newline$ Answer:

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Algebra 1

Solve linear equations: mixed review

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Q. Solve for the exact value of

x

\newline

3 \ln (2 x+7)+14=20

\newline

Answer:

Isolate natural logarithm term: First, we need to isolate the natural logarithm term by subtracting $14$ from both sides of the equation. $\newline$ $3\ln(2x+7) + 14 - 14 = 20 - 14$
Simplify by subtraction: Now, we simplify the equation by performing the subtraction. $3\ln(2x+7) = 6$
Divide to isolate logarithm: Next, we divide both sides of the equation by $3$ to isolate the natural logarithm. $\newline$ $\frac{3\ln(2x+7)}{3} = \frac{6}{3}$
Get logarithm by itself: After dividing, we get the natural logarithm by itself. $\ln(2x+7) = 2$
Exponentiate using base e: To eliminate the natural logarithm, we will exponentiate both sides of the equation using the base e. $e^{\ln(2x+7)} = e^2$
Simplify left side: Since $e^{\ln(x)} = x$ for any $x$ , we can simplify the left side of the equation. $\newline$ $2x+7 = e^2$
Isolate term with x: Now, we subtract $7$ from both sides to isolate the term with $x$ . $\newline$ $2x + 7 - 7 = e^2 - 7$
Simplify by subtraction: Simplify the equation by performing the subtraction. $2x = e^2 - 7$
Divide to solve for x: Finally, we divide both sides by $2$ to solve for $x$ . $\frac{2x}{2} = \frac{e^2 - 7}{2}$
Get exact value of x: After dividing, we get the exact value of x. $\newline$ $x = \frac{e^2 - 7}{2}$