Solve for x 3^(-x)=1/81

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

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

$- x = - 4$

Step 5

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 $- 1$ .

$x = 4$