Finite Math Examples

$2 = 4^{4 x + 4}$

Step 1

Rewrite the equation as $4^{4 x + 4} = 2$ .

$4^{4 x + 4} = 2$

Step 2

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

$2^{2 (4 x + 4)} = 2^{1}$

Step 3

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

$2 (4 x + 4) = 1$

Step 4

Solve for $x$ .

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Step 4.1

Divide each term in $2 (4 x + 4) = 1$ by $2$ and simplify.

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Step 4.1.1

Divide each term in $2 (4 x + 4) = 1$ by $2$ .

$\frac{2 (4 x + 4)}{2} = \frac{1}{2}$

Step 4.1.2

Simplify the left side.

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Step 4.1.2.1

Cancel the common factor of $2$ .

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Step 4.1.2.1.1

Cancel the common factor.

$\frac{2 (4 x + 4)}{2} = \frac{1}{2}$

Step 4.1.2.1.2

Divide $4 x + 4$ by $1$ .

$4 x + 4 = \frac{1}{2}$

Step 4.2

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

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Step 4.2.1

Subtract $4$ from both sides of the equation.

$4 x = \frac{1}{2} - 4$

Step 4.2.2

To write $- 4$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 4.2.3

Combine $- 4$ and $\frac{2}{2}$ .

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

Step 4.2.4

Combine the numerators over the common denominator.

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

Step 4.2.5

Simplify the numerator.

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Step 4.2.5.1

Multiply $- 4$ by $2$ .

$4 x = \frac{1 - 8}{2}$

Step 4.2.5.2

Subtract $8$ from $1$ .

$4 x = \frac{- 7}{2}$

Step 4.2.6

Move the negative in front of the fraction.

$4 x = - \frac{7}{2}$

Step 4.3

Divide each term in $4 x = - \frac{7}{2}$ by $4$ and simplify.

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Step 4.3.1

Divide each term in $4 x = - \frac{7}{2}$ by $4$ .

$\frac{4 x}{4} = \frac{- \frac{7}{2}}{4}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $4$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{- \frac{7}{2}}{4}$

Step 4.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- \frac{7}{2}}{4}$

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Multiply the numerator by the reciprocal of the denominator.

$x = - \frac{7}{2} \cdot \frac{1}{4}$

Step 4.3.3.2

Multiply $- \frac{7}{2} \cdot \frac{1}{4}$ .

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Step 4.3.3.2.1

Multiply $\frac{1}{4}$ by $\frac{7}{2}$ .

$x = - \frac{7}{4 \cdot 2}$

Step 4.3.3.2.2

Multiply $4$ by $2$ .

$x = - \frac{7}{8}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{7}{8}$

Decimal Form:

$x = - 0.875$