Evaluate 5^(-3x-1)=25

$5^{- 3 x - 1} = 25$

Step 1

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

$5^{- 3 x - 1} = 5^{2}$

Step 2

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

$- 3 x - 1 = 2$

Step 3

Solve for $x$ .

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

Add $1$ to both sides of the equation.

$- 3 x = 2 + 1$

Add $2$ and $1$ .

$- 3 x = 3$

Divide each term in $- 3 x = 3$ by $- 3$ and simplify.

Divide each term in $- 3 x = 3$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{3}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{3}{- 3}$

Divide $x$ by $1$ .

$x = \frac{3}{- 3}$

Simplify the right side.

Divide $3$ by $- 3$ .

$x = - 1$