Answer
x = 0.532
Explanation
The question requires that we solve for x, given the equation
[tex]-7e^{3x+1}-2=-96[/tex]
To solve this, we will first reduce the expression to having the term with power alone on one side
[tex]\begin{gathered} -7e^{3x+1}-2=-96 \\ -7e^{3x+1}=-96+2 \\ -7e^{3x+1}=-94 \\ \text{Divide both sides by -7} \\ \frac{-7e^{3x+1}}{-7}=\frac{-94}{-7} \\ e^{3x+1}=13.43 \end{gathered}[/tex]
The next step now is to take the natural logarithms of both sides
Note that taking the natural logarithms of e, gives 1. That is,
In e = 1
[tex]\begin{gathered} e^{3x+1}=13.43 \\ In(e^{3x+1})=In(13.43)^{}\text{ } \\ (3x+1)(In\text{ e) = }2.60 \\ (3x+1)(1)=2.60 \\ 3x+1=2.60 \end{gathered}[/tex]
3x + 1 = 2.60
3x = 2.60 - 1
3x = 1.60
Divide both sides by 3
(3x/3) = (1.60/3)
x = 0.532
Hope this Helps!!!
