Solve for x 6^(2x-3)=6^(-2x+1)

$6^{2 x - 3} = 6^{- 2 x + 1}$

Step 1

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

$6^{2 x - 3} = 6^{- 2 x + 1}$

Step 2

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

$2 x - 3 = - 2 x + 1$

Step 3

Solve for $x$ .

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

Add $2 x$ to both sides of the equation.

$2 x - 3 + 2 x = 1$

Add $2 x$ and $2 x$ .

$4 x - 3 = 1$

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

Add $3$ to both sides of the equation.

$4 x = 1 + 3$

Add $1$ and $3$ .

$4 x = 4$

Divide each term in $4 x = 4$ by $4$ and simplify.

Divide each term in $4 x = 4$ by $4$ .

$\frac{4 x}{4} = \frac{4}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{4}{4}$

Divide $x$ by $1$ .

$x = \frac{4}{4}$

Simplify the right side.

Divide $4$ by $4$ .

$x = 1$