Solve for x (x-3)^(2x-1)=(x-3)^(x+1)

${(x - 3)}^{2 x - 1} = {(x - 3)}^{x + 1}$

Step 1

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

${(x - 3)}^{2 x - 1} = {(x - 3)}^{x + 1}$

Step 2

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

$2 x - 1 = x + 1$

Step 3

Solve for $x$ .

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

Subtract $x$ from both sides of the equation.

$2 x - 1 - x = 1$

Subtract $x$ from $2 x$ .

$x - 1 = 1$

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

Add $1$ to both sides of the equation.

$x = 1 + 1$

Add $1$ and $1$ .

$x = 2$