Solve for the exact value of x. 6ln(4x+9)+4=-14 Answer:

Isolate natural logarithm term: First, we need to isolate the natural logarithm term on one side of the equation. We can do this by subtracting 4 from both sides of the equation. 6ln(4x+9) + 4 - 4 = -14 - 4 6ln(4x+9) = -18Divide by 6: Next, we divide both sides of the equation by 6 to solve for the natural logarithm of (4x+9). 6ln(4x+9) / 6 = -18 / 6 ln(4x+9) = -3Exponentiate to remove ln: Now, we will exponentiate both sides of the equation to remove the natural logarithm. We use the property that e^(ln(x)) = x. e^(ln(4x+9)) = e^(-3) 4x+9 = e^(-3)Subtract 9: We then subtract 9 from both sides of the equation to isolate the term with x. 4x+9 - 9 = e^(-3) - 9 4x = e^(-3) - 9Divide by 4: Finally, we divide both sides by 4 to solve for x. 4x / 4 = (e^(-3) - 9) / 4 x = (e^(-3) - 9) / 4

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Solve for the exact value of
x.

6ln(4x+9)+4=-14
Answer:

Solve for the exact value of $x$ . $\newline$ $6 \ln (4 x+9)+4=-14$ $\newline$ Answer:

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Grade 8

Solve equations with variables on both sides: fractional coefficients

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Q. Solve for the exact value of

x

\newline

6 \ln (4 x+9)+4=-14

\newline

Answer:

Isolate natural logarithm term: First, we need to isolate the natural logarithm term on one side of the equation. We can do this by subtracting $4$ from both sides of the equation. $\newline$ $6\ln(4x+9) + 4 - 4 = -14 - 4$ $\newline$ $6\ln(4x+9) = -18$
Divide by $6$ : Next, we divide both sides of the equation by $6$ to solve for the natural logarithm of $(4x+9)$ . $\frac{6\ln(4x+9)}{6} = \frac{-18}{6}$ $\ln(4x+9) = -3$
Exponentiate to remove ln: Now, we will exponentiate both sides of the equation to remove the natural logarithm. We use the property that $e^{\ln(x)} = x$ . $\newline$ $e^{\ln(4x+9)} = e^{-3}$ $\newline$ $4x+9 = e^{-3}$
Subtract $9$ : We then subtract $9$ from both sides of the equation to isolate the term with $x$ . $\newline$ $4x+9 - 9 = e^{-3} - 9$ $\newline$ $4x = e^{-3} - 9$
Divide by $4$ : Finally, we divide both sides by $4$ to solve for $x$ . $\frac{4x}{4} = \frac{e^{(-3)} - 9}{4}$ $x = \frac{e^{(-3)} - 9}{4}$