Solve for the exact value of x. 4ln(5x-6)+10=18 Answer:

Isolate natural logarithm term: Isolate the natural logarithm term by subtracting 10 from both sides of the equation. 4ln(5x-6) + 10 - 10 = 18 - 10 4ln(5x-6) = 8Divide by 4: Divide both sides of the equation by 4 to solve for the natural logarithm of (5x-6). (4ln(5x-6))/4 = 8/4 ln(5x-6) = 2Exponentiate to remove ln: Exponentiate both sides of the equation to remove the natural logarithm, using the property e^(ln(x)) = x. e^(ln(5x-6)) = e^2 5x - 6 = e^2Add 6 to isolate x: Add 6 to both sides of the equation to isolate the term with x. 5x - 6 + 6 = e^2 + 6 5x = e^2 + 6Divide by 5 to solve x: Divide both sides of the equation by 5 to solve for x. 5x/5 = (e^2 + 6)/5 x = (e^2 + 6)/5

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Q. Solve for the exact value of

x

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4 \ln (5 x-6)+10=18

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Answer:

Isolate natural logarithm term: Isolate the natural logarithm term by subtracting $10$ from both sides of the equation. $\newline$ $4\ln(5x-6) + 10 - 10 = 18 - 10$ $\newline$ $4\ln(5x-6) = 8$
Divide by $4$ : Divide both sides of the equation by $4$ to solve for the natural logarithm of $(5x-6)$ . $\frac{4\ln(5x-6)}{4} = \frac{8}{4}$ $\ln(5x-6) = 2$
Exponentiate to remove ln: Exponentiate both sides of the equation to remove the natural logarithm, using the property $e^{\ln(x)} = x$ . $\newline$ $e^{\ln(5x-6)} = e^2$ $\newline$ $5x - 6 = e^2$
Add $6$ to isolate x: Add $6$ to both sides of the equation to isolate the term with $x$ . $5x - 6 + 6 = e^2 + 6$ $5x = e^2 + 6$
Divide by $5$ to solve $x$ : Divide both sides of the equation by $5$ to solve for $x$ . $\frac{5x}{5} = \frac{(e^2 + 6)}{5}$ $x = \frac{(e^2 + 6)}{5}$