Solve for x 3^(-x)=81

$3^{- x} = 81$

Step 1

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

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

Step 2

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

$- x = 4$

Step 3

Divide each term in $- x = 4$ by $- 1$ and simplify.

Divide each term in $- x = 4$ by $- 1$ .

$\frac{- x}{- 1} = \frac{4}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{4}{- 1}$

Divide $x$ by $1$ .

$x = \frac{4}{- 1}$

Simplify the right side.

Divide $4$ by $- 1$ .

$x = - 4$