Question

I just need help simplifying it into a single exponential expression. Thank you

Answer 1

x = -½

Step-by-step explanation

To answer this, we will use the laws of indices to solve the left hand side

When the same variable, carrying different powers are multiplied with each other, then, the result is that same variable raised to the power of the sum of the two powers from before multiplication.

`\begin{gathered} e^xe^(x+1)=1 \\ e^(x+x+1)=1 \\ e^(2x+1)=1 \end{gathered}`

Take the natural logarithms of both sides

`\begin{gathered} e^(2x+1)=1 \\ In(e^(2x+1))=In(1) \\ (2x+1)(\text{In e) = In 1} \\ In\text{ e = 1, In 1 = 0} \\ (2x+1)(1)=0 \\ 2x+1=0 \end{gathered}`

2x + 1 = 0

2x = -1

Divide both sides by 2

(2x/2) = (-1/2)

x = (-1/2)

x = -½

Hope this Helps!!!