Solve for the exact value of x. 2ln(8x+1)+14=30 Answer:

Isolate logarithmic expression: First, we need to isolate the logarithmic expression by subtracting 14 from both sides of the equation. 2ln(8x+1) + 14 - 14 = 30 - 14 2ln(8x+1) = 16Divide by 2: Next, we divide both sides of the equation by 2 to solve for the natural logarithm of (8x+1). (2ln(8x+1)) / 2 = 16 / 2 ln(8x+1) = 8Exponentiate 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(8x+1)) = e^8 8x+1 = e^8Subtract 1: Subtract 1 from both sides to isolate the term with x. 8x + 1 - 1 = e^8 - 1 8x = e^8 - 1Divide by 8: Finally, divide both sides by 8 to solve for x. 8x / 8 = (e^8 - 1) / 8 x = (e^8 - 1) / 8

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Solve for the exact value of
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2ln(8x+1)+14=30
Answer:

Solve for the exact value of $x$ . $\newline$ $2 \ln (8 x+1)+14=30$ $\newline$ Answer:

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Algebra 1

Write a quadratic function from its x-intercepts and another point

Full solution

Q. Solve for the exact value of

x

\newline

2 \ln (8 x+1)+14=30

\newline

Answer:

Isolate logarithmic expression: First, we need to isolate the logarithmic expression by subtracting $14$ from both sides of the equation. $\newline$ $2\ln(8x+1) + 14 - 14 = 30 - 14$ $\newline$ $2\ln(8x+1) = 16$
Divide by $2$ : Next, we divide both sides of the equation by $2$ to solve for the natural logarithm of $(8x+1)$ . $\frac{2\ln(8x+1)}{2} = \frac{16}{2}$ $\ln(8x+1) = 8$
Exponentiate to remove ln: Now, we will exponentiate both sides of the equation to remove the natural logarithm. We use the property that $e^{\ln(x)} = x$ . $\newline$ $e^{\ln(8x+1)} = e^8$ $\newline$ $8x+1 = e^8$
Subtract $1$ : Subtract $1$ from both sides to isolate the term with $x$ . $\newline$ $8x + 1 - 1 = e^8 - 1$ $\newline$ $8x = e^8 - 1$
Divide by $8$ : Finally, divide both sides by $8$ to solve for x. $\newline$ $\frac{8x}{8} = \frac{e^8 - 1}{8}$ $\newline$ $x = \frac{e^8 - 1}{8}$