Finite Math Examples

$4^{x} + 2^{x + 2} = \frac{9}{4}$

Step 1

Subtract $\frac{9}{4}$ from both sides of the equation.

$4^{x} + 2^{x + 2} - \frac{9}{4} = 0$

Step 2

Simplify $4^{x} + 2^{x + 2} - \frac{9}{4}$ .

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Step 2.1

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

$4^{x} + 2^{x + 2} \cdot \frac{4}{4} - \frac{9}{4} = 0$

Step 2.2

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

$4^{x} + \frac{2^{x + 2} \cdot 4}{4} - \frac{9}{4} = 0$

Step 2.3

Combine the numerators over the common denominator.

$4^{x} + \frac{2^{x + 2} \cdot 4 - 9}{4} = 0$

Step 2.4

Multiply $2^{x + 2} \cdot 4$ .

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Step 2.4.1

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

$4^{x} + \frac{2^{x + 2} \cdot 2^{2} - 9}{4} = 0$

Step 2.4.2

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

$4^{x} + \frac{2^{x + 2 + 2} - 9}{4} = 0$

Step 2.4.3

Add $2$ and $2$ .

$4^{x} + \frac{2^{x + 4} - 9}{4} = 0$

Step 3

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.