Finite Math Examples

$y = 4 \cdot {(\frac{1}{2})}^{x - 2} - 2$

Step 1

Set $4 \cdot {(\frac{1}{2})}^{x - 2} - 2$ equal to $0$ .

$4 \cdot {(\frac{1}{2})}^{x - 2} - 2 = 0$

Step 2

Solve for $x$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the product rule to $\frac{1}{2}$ .

$4 \cdot \frac{1^{x - 2}}{2^{x - 2}} - 2 = 0$

Step 2.1.2

One to any power is one.

$4 \cdot \frac{1}{2^{x - 2}} - 2 = 0$

Step 2.1.3

Combine $4$ and $\frac{1}{2^{x - 2}}$ .

$\frac{4}{2^{x - 2}} - 2 = 0$

Step 2.2

Add $2$ to both sides of the equation.

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

Step 2.3

Move $2^{x - 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$4 \cdot 2^{- (x - 2)} = 2$

Step 2.4

Rewrite $4$ as $2^{2}$ .

$2^{2} \cdot 2^{- (x - 2)} = 2$

Step 2.5

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 2.6

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

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

Step 2.7

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

$2 - (x - 2) = 1$

Step 2.8

Solve for $x$ .

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Step 2.8.1

Simplify $2 - (x - 2)$ .

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Step 2.8.1.1

Simplify each term.

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Step 2.8.1.1.1

Apply the distributive property.

$2 - x - - 2 = 1$

Step 2.8.1.1.2

Multiply $- 1$ by $- 2$ .

$2 - x + 2 = 1$

Step 2.8.1.2

Add $2$ and $2$ .

$- x + 4 = 1$

Step 2.8.2

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

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Step 2.8.2.1

Subtract $4$ from both sides of the equation.

$- x = 1 - 4$

Step 2.8.2.2

Subtract $4$ from $1$ .

$- x = - 3$

Step 2.8.3

Divide each term in $- x = - 3$ by $- 1$ and simplify.

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Step 2.8.3.1

Divide each term in $- x = - 3$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 3}{- 1}$

Step 2.8.3.2

Simplify the left side.

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Step 2.8.3.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 3}{- 1}$

Step 2.8.3.2.2

Divide $x$ by $1$ .

$x = \frac{- 3}{- 1}$

Step 2.8.3.3

Simplify the right side.

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Step 2.8.3.3.1

Divide $- 3$ by $- 1$ .

$x = 3$

Step 3