Solve for the exact value of x. 6ln(8x-5)+10=52 Answer:

Isolate natural logarithm term: First, isolate the natural logarithm term by subtracting 10 from both sides of the equation. 6ln(8x-5) + 10 - 10 = 52 - 10 6ln(8x-5) = 42Divide by 6: Next, divide both sides of the equation by 6 to solve for the natural logarithm of (8x-5). (6ln(8x-5))/6 = 42/6 ln(8x-5) = 7Exponentiate to remove ln: Now, exponentiate both sides of the equation to remove the natural logarithm, using the property e^(ln(x)) = x. e^(ln(8x-5)) = e^7 8x-5 = e^7Add 5 to isolate x: Add 5 to both sides of the equation to isolate the term with x. 8x-5+5 = e^7+5 8x = e^7+5Divide by 8 to solve for x: Finally, divide both sides by 8 to solve for x. 8x/8 = (e^7+5)/8 x = (e^7+5)/8

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Solve for the exact value of
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6ln(8x-5)+10=52
Answer:

Solve for the exact value of $x$ . $\newline$ $6 \ln (8 x-5)+10=52$ $\newline$ Answer:

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Algebra 2

Composition of linear and quadratic functions: find a value

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Q. Solve for the exact value of

x

\newline

6 \ln (8 x-5)+10=52

\newline

Answer:

Isolate natural logarithm term: First, isolate the natural logarithm term by subtracting $10$ from both sides of the equation. $\newline$ $6\ln(8x-5) + 10 - 10 = 52 - 10$ $\newline$ $6\ln(8x-5) = 42$
Divide by $6$ : Next, divide both sides of the equation by $6$ to solve for the natural logarithm of $(8x-5)$ . $\frac{6\ln(8x-5)}{6} = \frac{42}{6}$ $\ln(8x-5) = 7$
Exponentiate to remove ln: Now, exponentiate both sides of the equation to remove the natural logarithm, using the property $e^{\ln(x)} = x$ . $\newline$ $e^{\ln(8x-5)} = e^7$ $\newline$ $8x-5 = e^7$
Add $5$ to isolate x: Add $5$ to both sides of the equation to isolate the term with $x$ . $8x-5+5 = e^7+5$ $8x = e^7+5$
Divide by $8$ to solve for x: Finally, divide both sides by $8$ to solve for x. $\newline$ $\frac{8x}{8} = \frac{e^7+5}{8}$ $\newline$ $x = \frac{e^7+5}{8}$