Solve the Rational Equation for x 5^(3-2x)=5^(-x)

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

Step 1

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

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

Step 2

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

$3 - 2 x = - x$

Step 3

Solve for $x$ .

Move all terms containing $x$ to the left side of the equation.

Add $x$ to both sides of the equation.

$3 - 2 x + x = 0$

Add $- 2 x$ and $x$ .

$3 - x = 0$

Subtract $3$ from both sides of the equation.

$- x = - 3$

Divide each term in $- x = - 3$ by $- 1$ and simplify.

Divide each term in $- x = - 3$ by $- 1$ .

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

Simplify the left side.

Dividing two negative values results in a positive value.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $- 3$ by $- 1$ .

$x = 3$