Precalculus Examples

$10 \log (10 \frac{80}{10})$

Step 1

Convert $10 \frac{80}{10}$ to an improper fraction.

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Step 1.1

A mixed number is an addition of its whole and fractional parts.

$10 \log (10 + \frac{80}{10})$

Step 1.2

Add $10$ and $\frac{80}{10}$ .

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Step 1.2.1

To write $10$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$10 \log (10 \cdot \frac{10}{10} + \frac{80}{10})$

Step 1.2.2

Combine $10$ and $\frac{10}{10}$ .

$10 \log (\frac{10 \cdot 10}{10} + \frac{80}{10})$

Step 1.2.3

Combine the numerators over the common denominator.

$10 \log (\frac{10 \cdot 10 + 80}{10})$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $10$ by $10$ .

$10 \log (\frac{100 + 80}{10})$

Step 1.2.4.2

Add $100$ and $80$ .

$10 \log (\frac{180}{10})$

Step 2

Divide $180$ by $10$ .

$10 \log (18)$

Step 3

Rewrite $\log (18)$ as $\log (2 \cdot 3^{2})$ .

$10 \log (2 \cdot 3^{2})$

Step 4

Rewrite $\log (2 \cdot 3^{2})$ as $\log (2) + \log (3^{2})$ .

$10 (\log (2) + \log (3^{2}))$

Step 5

Expand $\log (3^{2})$ by moving $2$ outside the logarithm.

$10 (\log (2) + 2 \log (3))$

Step 6

Apply the distributive property.

$10 \log (2) + 10 (2 \log (3))$

Step 7

Multiply $2$ by $10$ .

$10 \log (2) + 20 \log (3)$