Question

I wasnt at school when my teacher taught this im not sure what to do

Answer 1

x = 0.532

Step-by-step explanation

The question requires that we solve for x, given the equation

`-7e^(3x+1)-2=-96`

To solve this, we will first reduce the expression to having the term with power alone on one side

`\begin{gathered} -7e^(3x+1)-2=-96 \\ -7e^(3x+1)=-96+2 \\ -7e^(3x+1)=-94 \\ \text{Divide both sides by -7} \\ (-7e^(3x+1))/(-7)=(-94)/(-7) \\ e^(3x+1)=13.43 \end{gathered}`

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

`\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}`

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!!!