Algebra Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

$x + 1 = - 1$

Step 4

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

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Step 4.1

Subtract $1$ from both sides of the equation.

$x = - 1 - 1$

Step 4.2

Subtract $1$ from $- 1$ .

$x = - 2$