Finite Math Examples

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

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

Step 1

Multiply both sides of the equation by

\frac{log (27)}{127^{2 - 37}}

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

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

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

Step 2

Simplify both sides of the equation.

Tap for more steps...

Step 2.1

Simplify the left side.

Tap for more steps...

Step 2.1.1

Simplify

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

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

Tap for more steps...

Step 2.1.1.1

Simplify terms.

Tap for more steps...

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)

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

Step 2.1.1.1.2

Cancel the common factor of

log (27)

$\log (27)$ .

Tap for more steps...

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.

Tap for more steps...

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.

Tap for more steps...

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.

Tap for more steps...

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

$127^{35}$ .

Tap for more steps...

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.

Tap for more steps...

Step 2.2.1

Simplify

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

Tap for more steps...

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.

Tap for more steps...

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.

Tap for more steps...

Step 3.2.1

Cancel the common factor of

$ps$ .

Tap for more steps...

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.

Tap for more steps...

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

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

Tap for more steps...

Step 4.1

Rewrite the expression.

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

Step 4.2

Convert

$ps$ to

$s$ .

Tap for more steps...

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.

Tap for more steps...

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.

Tap for more steps...

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

$1$ .

Tap for more steps...

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

$127^{35} p \log (10460353203)$ .

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