Finite Math Examples

$30988 = (\frac{1 + \frac{x}{4^{20}} - 1}{\frac{x}{4}})$

Step 1

Rewrite the equation as $\frac{1 + \frac{x}{4^{20}} - 1}{\frac{x}{4}} = 30988$ .

$\frac{1 + \frac{x}{4^{20}} - 1}{\frac{x}{4}} = 30988$

Step 2

Factor each term.

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Step 2.1

Subtract $1$ from $1$ .

$\frac{\frac{x}{4^{20}} + 0}{\frac{x}{4}} = 30988$

Step 2.2

Add $\frac{x}{4^{20}}$ and $0$ .

$\frac{\frac{x}{4^{20}}}{\frac{x}{4}} = 30988$

Step 2.3

Multiply the numerator by the reciprocal of the denominator.

$\frac{x}{4^{20}} \cdot \frac{4}{x} = 30988$

Step 2.4

Combine.

$\frac{x \cdot 4}{4^{20} x} = 30988$

Step 2.5

Cancel the common factor of $x$ .

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Step 2.5.1

Cancel the common factor.

$\frac{x \cdot 4}{4^{20} x} = 30988$

Step 2.5.2

Rewrite the expression.

$\frac{4}{4^{20}} = 30988$

Step 2.6

Cancel the common factor of $4$ and $4^{20}$ .

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Step 2.6.1

Factor $4$ out of $4$ .

$\frac{4 (1)}{4^{20}} = 30988$

Step 2.6.2

Cancel the common factors.

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Step 2.6.2.1

Factor $4$ out of $4^{20}$ .

$\frac{4 (1)}{4 \cdot 4^{19}} = 30988$

Step 2.6.2.2

Cancel the common factor.

$\frac{4 \cdot 1}{4 \cdot 4^{19}} = 30988$

Step 2.6.2.3

Rewrite the expression.

$\frac{1}{4^{19}} = 30988$

Step 2.7

Raise $4$ to the power of $19$ .

$\frac{1}{274877906944} = 30988$

Step 3

Since $\frac{1}{274877906944} \neq 30988$ , there are no solutions.

No solution