Algebra Examples

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

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 $x$ .

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Step 3.1

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

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Step 3.1.1

Subtract $1$ from both sides of the equation.

$- 2 x = 5 - 1$

Step 3.1.2

Subtract $1$ from $5$ .

$- 2 x = 4$

Step 3.2

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

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Step 3.2.1

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

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

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $- 2$ .

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Step 3.2.2.1.1

Cancel the common factor.

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

Step 3.2.2.1.2

Divide $x$ by $1$ .

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

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide $4$ by $- 2$ .

$x = - 2$