what is the value of x in the equation below? 1 + 2e^{x + 1}=9\nx = log4 - 1\nx = log4\nx = ln4 - 1\nx = ln4

Explanation:

Step1: Isolate the exponential term

Subtract 1 from both sides of the equation $1 + 2e^{x + 1}=9$. $2e^{x + 1}=9 - 1=8$. Then divide both sides by 2: $e^{x + 1}=\frac{8}{2}=4$.

Step2: Apply natural - logarithm

Take the natural logarithm of both sides of the equation $e^{x + 1}=4$. Since $\ln(e^{a})=a$, we have $\ln(e^{x + 1})=\ln(4)$. So $x + 1=\ln(4)$.

Step3: Solve for x

Subtract 1 from both sides to get $x=\ln(4)-1$.

Answer:

C. $x=\ln4 - 1$