Finite Math Examples

$\frac{127^{2 - 37} x (ps)}{\log (27)} = 7 p$

Step 1

Multiply both sides of the equation by $\frac{\log (27)}{127^{2 - 37}}$ .

$\frac{\log (27)}{127^{2 - 37}} \cdot \frac{127^{2 - 37} x ps}{\log (27)} = \frac{\log (27)}{127^{2 - 37}} (7 p)$

Step 2

Simplify both sides of the equation.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $\frac{\log (27)}{127^{2 - 37}} \cdot \frac{127^{2 - 37} x ps}{\log (27)}$ .

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Step 2.1.1.1

Simplify terms.

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Step 2.1.1.1.1

Combine.

$\frac{\log (27) (127^{2 - 37} x ps)}{127^{2 - 37} \log (27)} = \frac{\log (27)}{127^{2 - 37}} (7 p)$

Step 2.1.1.1.2

Cancel the common factor of $\log (27)$ .

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Step 2.1.1.1.2.1

Cancel the common factor.

$\frac{\log (27) (127^{2 - 37} x ps)}{127^{2 - 37} \log (27)} = \frac{\log (27)}{127^{2 - 37}} (7 p)$

Step 2.1.1.1.2.2

Rewrite the expression.

$\frac{127^{2 - 37} x ps}{127^{2 - 37}} = \frac{\log (27)}{127^{2 - 37}} (7 p)$

Step 2.1.1.2

Simplify the numerator.

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Step 2.1.1.2.1

Subtract $37$ from $2$ .

$\frac{127^{- 35} x ps}{127^{2 - 37}} = \frac{\log (27)}{127^{2 - 37}} (7 p)$

Step 2.1.1.2.2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{\frac{1}{127^{35}} x ps}{127^{2 - 37}} = \frac{\log (27)}{127^{2 - 37}} (7 p)$

Step 2.1.1.2.3

Combine exponents.

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Step 2.1.1.2.3.1

Combine $\frac{1}{127^{35}}$ and $x$ .

$\frac{\frac{x}{127^{35}} ps}{127^{2 - 37}} = \frac{\log (27)}{127^{2 - 37}} (7 p)$

Step 2.1.1.2.3.2

Combine $\frac{x}{127^{35}}$ and $ps$ .

$\frac{\frac{x ps}{127^{35}}}{127^{2 - 37}} = \frac{\log (27)}{127^{2 - 37}} (7 p)$

Step 2.1.1.3

Simplify the denominator.

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Step 2.1.1.3.1

Subtract $37$ from $2$ .

$\frac{\frac{x ps}{127^{35}}}{127^{- 35}} = \frac{\log (27)}{127^{2 - 37}} (7 p)$

Step 2.1.1.3.2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{\frac{x ps}{127^{35}}}{\frac{1}{127^{35}}} = \frac{\log (27)}{127^{2 - 37}} (7 p)$

Step 2.1.1.4

Multiply the numerator by the reciprocal of the denominator.

$\frac{x ps}{127^{35}} \cdot 127^{35} = \frac{\log (27)}{127^{2 - 37}} (7 p)$

Step 2.1.1.5

Cancel the common factor of $127^{35}$ .

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Step 2.1.1.5.1

Cancel the common factor.

$\frac{x ps}{127^{35}} \cdot 127^{35} = \frac{\log (27)}{127^{2 - 37}} (7 p)$

Step 2.1.1.5.2

Rewrite the expression.

$x ps = \frac{\log (27)}{127^{2 - 37}} (7 p)$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $\frac{\log (27)}{127^{2 - 37}} (7 p)$ .

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Step 2.2.1.1

Move $127^{2 - 37}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$x ps = \log (27) \cdot 127^{- (2 - 37)} (7 p)$

Step 2.2.1.2

Subtract $37$ from $2$ .

$x ps = \log (27) \cdot 127^{- - 35} (7 p)$

Step 2.2.1.3

Multiply $- 1$ by $- 35$ .

$x ps = \log (27) \cdot 127^{35} (7 p)$

Step 2.2.1.4

Move $7$ to the left of $\log (27) \cdot 127^{35}$ .

$x ps = 7 \cdot (\log (27) \cdot 127^{35}) p$

Step 2.2.1.5

Reorder factors in $7 \log (27) \cdot 127^{35} p$ .

$x ps = 7 \cdot 127^{35} p \log (27)$

Step 3

Divide each term in $x ps = 7 \cdot (127^{35} p \log (27))$ by $ps$ and simplify.

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Step 3.1

Divide each term in $x ps = 7 \cdot (127^{35} p \log (27))$ by $ps$ .

$\frac{x ps}{ps} = \frac{7 \cdot (127^{35} p \log (27))}{ps}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $ps$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{x ps}{ps} = \frac{7 \cdot (127^{35} p \log (27))}{ps}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{7 \cdot (127^{35} p \log (27))}{ps}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify $7 \log (27)$ by moving $7$ inside the logarithm.

$x = \frac{127^{35} p \log (27^{7})}{ps}$

Step 3.3.2

Raise $27$ to the power of $7$ .

$x = \frac{127^{35} p \log (10460353203)}{ps}$

Step 4

Simplify $x = \frac{127^{35} p \log (10460353203)}{ps}$ .

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Step 4.1

Rewrite the expression.

$x = 127^{35} p \log (10460353203) \frac{1}{ps}$

Step 4.2

Convert $ps$ to $s$ .

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Step 4.2.1

Convert $ps$ to $s$ .

$x = 127^{35} p \log (10460353203) (\frac{1}{ps} \times \frac{1000000000000 ps}{1 s})$

Step 4.2.2

Cancel the common units and simplify.

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Step 4.2.2.1

Cross cancel units.

$x = 127^{35} p \log (10460353203) (\frac{1}{ps} \times \frac{1000000000000 ps}{1 s})$

Step 4.2.2.2

Simplify the expression.

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Step 4.2.2.2.1

Remove the canceled units.

$x = 127^{35} p \log (10460353203) (\frac{1}{1} \times \frac{1000000000000}{1 s})$

Step 4.2.2.2.2

Cancel the common factor of $1$ .

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Step 4.2.2.2.2.1

Cancel the common factor.

$x = 127^{35} p \log (10460353203) (\frac{1}{1} \times \frac{1000000000000}{1 s})$

Step 4.2.2.2.2.2

Rewrite the expression.

$x = 127^{35} p \log (10460353203) (1 \times \frac{1000000000000}{1 s})$

Step 4.2.2.2.3

Multiply $\frac{1000000000000}{1 s}$ by $1$ .

$x = 127^{35} p \log (10460353203) \frac{1000000000000}{1 s}$

Step 4.2.2.2.4

Rewrite the expression.

$x = 127^{35} p \log (10460353203) (1000000000000 \frac{1}{s})$

Step 4.3

Rewrite $\frac{1}{s}$ as $Hz$ .

$x = 127^{35} p \log (10460353203) (1000000000000 Hz)$

Step 4.4

Move $1000000000000$ to the left of $127^{35} p \log (10460353203)$ .

$x = 1000000000000 \cdot 127^{35} p \log (10460353203) Hz$