Solve for \( x: 2 e^{x+1}-6=10 \) \( \begin{array}{lll}1.079 & \text { b. } & 3.079 \\ 2,979.958 & \text { d. } & 2,981.958\end{array} \)

Solve the equation \( 2e^{x+1}-6=10 \). Solve the equation by following steps: - step0: Solve for \(x\): \(2e^{x+1}-6=10\) - step1: Move the expression to the left side: \(2e^{x+1}-6-10=0\) - step2: Subtract the numbers: \(2e^{x+1}-16=0\) - step3: Rewrite the expression: \(2e^{x+1}=16\) - step4: Divide both sides: \(\frac{2e^{x+1}}{2}=\frac{16}{2}\) - step5: Divide the numbers: \(e^{x+1}=8\) - step6: Take the logarithm of both sides: \(\ln{\left(e^{x+1}\right)}=\ln{\left(8\right)}\) - step7: Evaluate the logarithm: \(x+1=\ln{\left(8\right)}\) - step8: Move the constant to the right side: \(x=\ln{\left(8\right)}-1\) - step9: Simplify: \(x=3\ln{\left(2\right)}-1\) The solution to the equation \(2e^{x+1}-6=10\) is \(x=3\ln{(2)}-1\). Now, let's calculate the value of \(3\ln{(2)}-1\) to determine which option is correct. Calculate the value by following steps: - step0: Calculate: \(3\ln{\left(2\right)}-1\) The value of \(3\ln{(2)}-1\) is approximately 1.079442. Therefore, the correct option is 1.079.