Finite Math Examples

f (x) = {(\frac{1}{2})}^{x} - 2

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

Step 1

Set

{(\frac{1}{2})}^{x} - 2

${(\frac{1}{2})}^{x} - 2$ equal to

0

$0$ .

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

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

Step 2

Solve for

x

$x$ .

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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}

$\frac{1}{2}$ .

\frac{1^{x}}{2^{x}} - 2 = 0

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

Step 2.1.2

One to any power is one.

\frac{1}{2^{x}} - 2 = 0

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

\frac{1}{2^{x}} - 2 = 0

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

Step 2.2

Add

2

$2$ to both sides of the equation.

\frac{1}{2^{x}} = 2

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

Step 2.3

Move

2^{x}

$2^{x}$ to the numerator using the negative exponent rule

\frac{1}{b^{- n}} = b^{n}

$\frac{1}{b^{- n}} = b^{n}$ .

2^{- x} = 2

$2^{- x} = 2$

Step 2.4

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

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

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

Step 2.5

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

- x = 1

$- x = 1$

Step 2.6

Divide each term in

- x = 1

$- x = 1$ by

- 1

$- 1$ and simplify.

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Step 2.6.1

Divide each term in

- x = 1

$- x = 1$ by

- 1

$- 1$ .

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

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

Step 2.6.2

Simplify the left side.

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Step 2.6.2.1

Dividing two negative values results in a positive value.

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

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

Step 2.6.2.2

Divide

x

$x$ by

1

$1$ .

x = \frac{1}{- 1}

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

x = \frac{1}{- 1}

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

Step 2.6.3

Simplify the right side.

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Step 2.6.3.1

Divide

1

$1$ by

- 1

$- 1$ .

x = - 1

$x = - 1$

x = - 1

$x = - 1$

x = - 1

$x = - 1$

x = - 1

$x = - 1$

Step 3