Solve for x e^x=1/(e^3)

$e^{x} = \frac{1}{e^{3}}$

Step 1

Move $e^{3}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$e^{x} = e^{- 3}$

Step 2

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

$x = - 3$