Precalculus Examples

$4^{1 - 2 x} = 2$

Step 1

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

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

Step 2

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

$2 (1 - 2 x) = 1$

Step 3

Solve for $x$ .

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Step 3.1

Divide each term in $2 (1 - 2 x) = 1$ by $2$ and simplify.

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Step 3.1.1

Divide each term in $2 (1 - 2 x) = 1$ by $2$ .

$\frac{2 (1 - 2 x)}{2} = \frac{1}{2}$

Step 3.1.2

Simplify the left side.

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Step 3.1.2.1

Cancel the common factor of $2$ .

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Step 3.1.2.1.1

Cancel the common factor.

$\frac{2 (1 - 2 x)}{2} = \frac{1}{2}$

Step 3.1.2.1.2

Divide $1 - 2 x$ by $1$ .

$1 - 2 x = \frac{1}{2}$

Step 3.2

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

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Step 3.2.1

Subtract $1$ from both sides of the equation.

$- 2 x = \frac{1}{2} - 1$

Step 3.2.2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- 2 x = \frac{1}{2} - 1 \cdot \frac{2}{2}$

Step 3.2.3

Combine $- 1$ and $\frac{2}{2}$ .

$- 2 x = \frac{1}{2} + \frac{- 1 \cdot 2}{2}$

Step 3.2.4

Combine the numerators over the common denominator.

$- 2 x = \frac{1 - 1 \cdot 2}{2}$

Step 3.2.5

Simplify the numerator.

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Step 3.2.5.1

Multiply $- 1$ by $2$ .

$- 2 x = \frac{1 - 2}{2}$

Step 3.2.5.2

Subtract $2$ from $1$ .

$- 2 x = \frac{- 1}{2}$

Step 3.2.6

Move the negative in front of the fraction.

$- 2 x = - \frac{1}{2}$

Step 3.3

Divide each term in $- 2 x = - \frac{1}{2}$ by $- 2$ and simplify.

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Step 3.3.1

Divide each term in $- 2 x = - \frac{1}{2}$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{- \frac{1}{2}}{- 2}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $- 2$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{- \frac{1}{2}}{- 2}$

Step 3.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- \frac{1}{2}}{- 2}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Multiply the numerator by the reciprocal of the denominator.

$x = - \frac{1}{2} \cdot \frac{1}{- 2}$

Step 3.3.3.2

Move the negative in front of the fraction.

$x = - \frac{1}{2} (- \frac{1}{2})$

Step 3.3.3.3

Multiply $- \frac{1}{2} (- \frac{1}{2})$ .

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Step 3.3.3.3.1

Multiply $- 1$ by $- 1$ .

$x = 1 (\frac{1}{2}) \frac{1}{2}$

Step 3.3.3.3.2

Multiply $\frac{1}{2}$ by $1$ .

$x = \frac{1}{2} \cdot \frac{1}{2}$

Step 3.3.3.3.3

Multiply $\frac{1}{2}$ by $\frac{1}{2}$ .

$x = \frac{1}{2 \cdot 2}$

Step 3.3.3.3.4

Multiply $2$ by $2$ .

$x = \frac{1}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{4}$

Decimal Form:

$x = 0.25$