Solve for the exact value of x. 5ln(8x+6)-12=3 Answer:

Isolate natural logarithm term: Isolate the natural logarithm term. We start by adding 12 to both sides of the equation to isolate the term with the natural logarithm. 5ln(8x+6) - 12 + 12 = 3 + 12 5ln(8x+6) = 15Divide sides to solve: Divide both sides by 5 to solve for the natural logarithm of the expression. 5ln(8x+6) / 5 = 15 / 5 ln(8x+6) = 3Exponentiate to remove logarithm: Exponentiate both sides to remove the natural logarithm. e^(ln(8x+6)) = e^3 8x+6 = e^3Subtract to solve for 8x: Subtract 6 from both sides to solve for 8x. 8x + 6 - 6 = e^3 - 6 8x = e^3 - 6Divide to solve for x: Divide both sides by 8 to solve for x. 8x / 8 = (e^3 - 6) / 8 x = (e^3 - 6) / 8

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Solve for the exact value of
x.

5ln(8x+6)-12=3
Answer:

Solve for the exact value of $x$ . $\newline$ $5 \ln (8 x+6)-12=3$ $\newline$ Answer:

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Q. Solve for the exact value of

x

\newline

5 \ln (8 x+6)-12=3

\newline

Answer:

Isolate natural logarithm term: Isolate the natural logarithm term. $\newline$ We start by adding $12$ to both sides of the equation to isolate the term with the natural logarithm. $\newline$ $5\ln(8x+6) - 12 + 12 = 3 + 12$ $\newline$ $5\ln(8x+6) = 15$
Divide sides to solve: Divide both sides by $5$ to solve for the natural logarithm of the expression. $\newline$ $\frac{5\ln(8x+6)}{5} = \frac{15}{5}$ $\newline$ $\ln(8x+6) = 3$
Exponentiate to remove logarithm: Exponentiate both sides to remove the natural logarithm. $\newline$ $e^{\ln(8x+6)} = e^3$ $\newline$ $8x+6 = e^3$
Subtract to solve for $8x$ : Subtract $6$ from both sides to solve for $8x$ . $8x + 6 - 6 = e^3 - 6$ $8x = e^3 - 6$
Divide to solve for x: Divide both sides by $8$ to solve for x. $\newline$ $\frac{8x}{8} = \frac{e^3 - 6}{8}$ $\newline$ $x = \frac{e^3 - 6}{8}$