Solve for the exact value of x. 5ln(5x-10)-14=-4 Answer:

Isolate natural logarithm term: Isolate the natural logarithm term. We start by adding 14 to both sides of the equation to isolate the term with the natural logarithm. 5ln(5x-10) - 14 + 14 = -4 + 14 5ln(5x-10) = 10Divide sides solve natural logarithm: Divide both sides by 5 to solve for the natural logarithm of (5x-10). 5ln(5x-10) / 5 = 10 / 5 ln(5x-10) = 2Exponentiate to remove logarithm: Exponentiate both sides to remove the natural logarithm. e^(ln(5x-10)) = e^2 5x - 10 = e^2Add 10 solve for 5x: Add 10 to both sides to solve for 5x. 5x - 10 + 10 = e^2 + 10 5x = e^2 + 10Divide sides solve for x: Divide both sides by 5 to solve for x. 5x / 5 = (e^2 + 10) / 5 x = (e^2 + 10) / 5

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Solve for the exact value of
x.

5ln(5x-10)-14=-4
Answer:

Solve for the exact value of $x$ . $\newline$ $5 \ln (5 x-10)-14=-4$ $\newline$ Answer:

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Q. Solve for the exact value of

x

\newline

5 \ln (5 x-10)-14=-4

\newline

Answer:

Isolate natural logarithm term: Isolate the natural logarithm term. $\newline$ We start by adding $14$ to both sides of the equation to isolate the term with the natural logarithm. $\newline$ $5\ln(5x-10) - 14 + 14 = -4 + 14$ $\newline$ $5\ln(5x-10) = 10$
Divide sides solve natural logarithm: Divide both sides by $5$ to solve for the natural logarithm of $(5x-10)$ . $\frac{5\ln(5x-10)}{5} = \frac{10}{5}$ $\ln(5x-10) = 2$
Exponentiate to remove logarithm: Exponentiate both sides to remove the natural logarithm. $\newline$ $e^{\ln(5x-10)} = e^2$ $\newline$ $5x - 10 = e^2$
Add $10$ solve for $5x$ : Add $10$ to both sides to solve for $5x$ . $\newline$ $5x - 10 + 10 = e^2 + 10$ $\newline$ $5x = e^2 + 10$
Divide sides solve for x: Divide both sides by $5$ to solve for $x$ . $\frac{5x}{5} = \frac{e^2 + 10}{5}$ $x = \frac{e^2 + 10}{5}$