what is the value of x if $e^{3x + 6}=8$?\n$x=\frac{ln8 - 6}{3}$\n$x=\frac{ln6 - 8}{3}$\n$x=\frac{ln8 +…

what is the value of x if $e^{3x + 6}=8$?\n$x=\frac{ln8 - 6}{3}$\n$x=\frac{ln6 - 8}{3}$\n$x=\frac{ln8 + 6}{3}$\n$x=\frac{ln6 + 8}{3}$

what is the value of x if $e^{3x + 6}=8$?\n$x=\frac{ln8 - 6}{3}$\n$x=\frac{ln6 - 8}{3}$\n$x=\frac{ln8 + 6}{3}$\n$x=\frac{ln6 + 8}{3}$

Answer

Explanation:

Step1: Apply natural - log to both sides

Take the natural logarithm of both sides of the equation $e^{3x + 6}=8$. Since $\ln(e^{a})=a$, we have $\ln(e^{3x + 6})=\ln(8)$, which simplifies to $3x + 6=\ln(8)$.

Step2: Isolate the term with x

Subtract 6 from both sides of the equation $3x + 6=\ln(8)$ to get $3x=\ln(8)-6$.

Step3: Solve for x

Divide both sides of the equation $3x=\ln(8)-6$ by 3. So, $x = \frac{\ln(8)-6}{3}$.

Answer:

A. $x=\frac{\ln8 - 6}{3}$