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Solve for the exact value of
x.

2ln(6x+5)-11=-3
Answer:

Solve for the exact value of $x$ . $\newline$ $2 \ln (6 x+5)-11=-3$ $\newline$ Answer:

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Solve equations with variables on both sides: fractional coefficients

Full solution

Q. Solve for the exact value of

x

.

\newline

2 \ln (6 x+5)-11=-3

\newline

Answer:

Isolate logarithmic expression: First, we need to isolate the logarithmic expression. To do this, we add $11$ to both sides of the equation. $\newline$ $2\ln(6x+5) - 11 + 11 = -3 + 11$ $\newline$ $2\ln(6x+5) = 8$
Divide by $2$ : Next, we divide both sides of the equation by $2$ to solve for the natural logarithm of $(6x+5)$ . $\frac{2\ln(6x+5)}{2} = \frac{8}{2}$ $\ln(6x+5) = 4$
Exponentiate to remove ln: Now, we will exponentiate both sides of the equation to remove the natural logarithm. We use the property that $e^{\ln(x)} = x$ . $e^{\ln(6x+5)} = e^4$ $6x+5 = e^4$
Subtract $5$ : We then subtract $5$ from both sides of the equation to isolate the term with $x$ . $\newline$ $6x + 5 - 5 = e^4 - 5$ $\newline$ $6x = e^4 - 5$
Divide by $6$ : Finally, we divide both sides by $6$ to solve for x. $\newline$ $\frac{6x}{6} = \frac{e^4 - 5}{6}$ $\newline$ $x = \frac{e^4 - 5}{6}$

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