Solve for x 3^x=1/81

$3^{x} = \frac{1}{81}$

Raise $81$ to the power of $1$ .

$3^{x} = \frac{1}{81^{1}}$

Move $81^{1}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$3^{x} = 81^{- 1}$

Create equivalent expressions in the equation that all have equal bases.

$3^{x} = 3^{- 4}$

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

$x = - 4$