Finite Math Examples

$L = 10 + \log (\frac{\frac{4.1 x \cdot 10^{- 6} W}{m^{2}}}{\frac{10^{- 12} W}{m^{2}}})$

Step 1

Remove parentheses.

$L = 10 + \log (\frac{\frac{4.1 x \cdot (10^{- 6} W)}{m^{2}}}{\frac{10^{- 12} W}{m^{2}}})$

Step 2

Remove parentheses.

$L = 10 + \log (\frac{\frac{4.1 x \cdot (10^{- 6} W)}{m^{2}}}{\frac{10^{- 12} W}{m^{2}}})$

Step 3

Simplify $10 + \log (\frac{\frac{4.1 x \cdot (10^{- 6} W)}{m^{2}}}{\frac{10^{- 12} W}{m^{2}}})$ .

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply the numerator by the reciprocal of the denominator.

$L = 10 + \log (\frac{4.1 x \cdot 10^{- 6} W}{m^{2}} \cdot \frac{m^{2}}{10^{- 12} W})$

Step 3.1.2

Combine.

$L = 10 + \log (\frac{4.1 x \cdot 10^{- 6} W m^{2}}{m^{2} (10^{- 12} W)})$

Step 3.1.3

Move $10^{- 12}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$L = 10 + \log (\frac{4.1 x \cdot 10^{- 6} W m^{2} \cdot 10^{12}}{m^{2} W})$

Step 3.1.4

Multiply $10^{- 6}$ by $10^{12}$ by adding the exponents.

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Step 3.1.4.1

Move $10^{12}$ .

$L = 10 + \log (\frac{4.1 x \cdot (10^{12} \cdot 10^{- 6}) W m^{2}}{m^{2} W})$

Step 3.1.4.2

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

$L = 10 + \log (\frac{4.1 x \cdot 10^{12 - 6} W m^{2}}{m^{2} W})$

Step 3.1.4.3

Subtract $6$ from $12$ .

$L = 10 + \log (\frac{4.1 x \cdot 10^{6} W m^{2}}{m^{2} W})$

Step 3.1.5

Cancel the common factor of $W$ .

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Step 3.1.5.1

Cancel the common factor.

$L = 10 + \log (\frac{4.1 x \cdot 10^{6} W m^{2}}{m^{2} W})$

Step 3.1.5.2

Rewrite the expression.

$L = 10 + \log (\frac{4.1 x \cdot 10^{6} m^{2}}{m^{2}})$

Step 3.1.6

Cancel the common factor of $m^{2}$ .

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Step 3.1.6.1

Cancel the common factor.

$L = 10 + \log (\frac{4.1 x \cdot 10^{6} m^{2}}{m^{2}})$

Step 3.1.6.2

Divide $4.1 x \cdot 10^{6}$ by $1$ .

$L = 10 + \log (4.1 x \cdot 10^{6})$

Step 3.1.7

Rewrite $\log (4.1 x \cdot 10^{6})$ as $\log (4.1 x) + \log (10^{6})$ .

$L = 10 + \log (4.1 x) + \log (10^{6})$

Step 3.1.8

Use logarithm rules to move $6$ out of the exponent.

$L = 10 + \log (4.1 x) + 6 \log (10)$

Step 3.1.9

Logarithm base $10$ of $10$ is $1$ .

$L = 10 + \log (4.1 x) + 6 \cdot 1$

Step 3.1.10

Multiply $6$ by $1$ .

$L = 10 + \log (4.1 x) + 6$

Step 3.2

Add $10$ and $6$ .

$L = 16 + \log (4.1 x)$