Solve for x 3^(1-2x)=243

$3^{1 - 2 x} = 243$

Step 1

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

$3^{1 - 2 x} = 3^{5}$

Step 2

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

$1 - 2 x = 5$

Step 3

Solve for $x$ .

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

Subtract $1$ from both sides of the equation.

$- 2 x = 5 - 1$

Subtract $1$ from $5$ .

$- 2 x = 4$

Divide each term in $- 2 x = 4$ by $- 2$ and simplify.

Divide each term in $- 2 x = 4$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{4}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{4}{- 2}$

Divide $x$ by $1$ .

$x = \frac{4}{- 2}$

Simplify the right side.

Divide $4$ by $- 2$ .

$x = - 2$