Solve for x e^(x+7)=1/e

$e^{x + 7} = \frac{1}{e}$

Step 1

Raise $e$ to the power of $1$ .

$e^{x + 7} = \frac{1}{e^{1}}$

Step 2

Move $e^{1}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$e^{x + 7} = e^{- 1}$

Step 3

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

$x + 7 = - 1$

Step 4

Move all terms not containing $x$ to the right side of the equation.

Subtract $7$ from both sides of the equation.

$x = - 1 - 7$

Subtract $7$ from $- 1$ .

$x = - 8$