Solve for x 5^(3-2x)=5^(-x)

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

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

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

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

$3 - 2 x = - x$

Solve for $x$ .

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

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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.

$- x = - 3$

Multiply each term in $- x = - 3$ by $- 1$

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

$(- x) \cdot - 1 = (- 3) \cdot - 1$

Multiply $(- x) \cdot - 1$ .

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Multiply $- 1$ by $- 1$ .

$1 x = (- 3) \cdot - 1$

Multiply $x$ by $1$ .

$x = (- 3) \cdot - 1$

Multiply $- 3$ by $- 1$ .

$x = 3$

Solve for x 5^(3-2x)=5^(-x)

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