Solve for x 8-3^x=-1

$8 - 3^{x} = - 1$

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

Subtract $8$ from both sides of the equation.

$- 3^{x} = - 1 - 8$

Subtract $8$ from $- 1$ .

$- 3^{x} = - 9$

Divide each term in $- 3^{x} = - 9$ by $- 1$ and simplify.

Divide each term in $- 3^{x} = - 9$ by $- 1$ .

$\frac{- 3^{x}}{- 1} = \frac{- 9}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{3^{x}}{1} = \frac{- 9}{- 1}$

Divide $3^{x}$ by $1$ .

$3^{x} = \frac{- 9}{- 1}$

Simplify the right side.

Divide $- 9$ by $- 1$ .

$3^{x} = 9$

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

$3^{x} = 3^{2}$

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

$x = 2$