Solve for the exact value of x. 4ln(6x-4)+7=15 Answer:

Subtract to isolate natural logarithm: Isolate the natural logarithm term by subtracting 7 from both sides of the equation. 4ln(6x-4) + 7 - 7 = 15 - 7Simplify by subtraction: Simplify the equation by performing the subtraction. 4ln(6x-4) = 8Divide to isolate logarithm: Divide both sides of the equation by 4 to isolate the natural logarithm. (4ln(6x-4))/4 = 8/4Simplify by division: Simplify the equation by performing the division. ln(6x-4) = 2Exponentiate to remove logarithm: Exponentiate both sides of the equation to remove the natural logarithm, using the property e^(ln(x)) = x. e^(ln(6x-4)) = e^2Simplify using logarithm property: Simplify the left side of the equation using the property of logarithms. 6x - 4 = e^2Addition to isolate x term: Add 4 to both sides of the equation to isolate the term with x. 6x - 4 + 4 = e^2 + 4Simplify by addition: Simplify the equation by performing the addition. 6x = e^2 + 4Divide to solve for x: Divide both sides of the equation by 6 to solve for x. x = (e^2 + 4)/6

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Solve for the exact value of
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4ln(6x-4)+7=15
Answer:

Solve for the exact value of $x$ . $\newline$ $4 \ln (6 x-4)+7=15$ $\newline$ Answer:

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Algebra 2

Simplify expressions using trigonometric identities

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Q. Solve for the exact value of

x

\newline

4 \ln (6 x-4)+7=15

\newline

Answer:

Subtract to isolate natural logarithm: Isolate the natural logarithm term by subtracting $7$ from both sides of the equation. $\newline$ $4\ln(6x-4) + 7 - 7 = 15 - 7$
Simplify by subtraction: Simplify the equation by performing the subtraction. $\newline$ $4\ln(6x-4) = 8$
Divide to isolate logarithm: Divide both sides of the equation by $4$ to isolate the natural logarithm. $\newline$ $\frac{4\ln(6x-4)}{4} = \frac{8}{4}$
Simplify by division: Simplify the equation by performing the division. $\newline$ $\ln(6x-4) = 2$
Exponentiate to remove logarithm: Exponentiate both sides of the equation to remove the natural logarithm, using the property $e^{\ln(x)} = x$ . $\newline$ $e^{\ln(6x-4)} = e^2$
Simplify using logarithm property: Simplify the left side of the equation using the property of logarithms. $6x - 4 = e^2$
Addition to isolate x term: Add $4$ to both sides of the equation to isolate the term with $x$ . $\newline$ $6x - 4 + 4 = e^2 + 4$
Simplify by addition: Simplify the equation by performing the addition. $6x = e^2 + 4$
Divide to solve for $x$ : Divide both sides of the equation by $6$ to solve for $x$ . $x = \frac{e^2 + 4}{6}$