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

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

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

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

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

$2 x = 3 x - 1$

Solve for $x$ .

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

Subtract $3 x$ from both sides of the equation.

$2 x - 3 x = - 1$

Subtract $3 x$ from $2 x$ .

$- x = - 1$

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

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

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

Simplify the left side.

Dividing two negative values results in a positive value.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $- 1$ by $- 1$ .

$x = 1$