Precalculus Examples

$\log (x) \cdot 20 + \log (x) \cdot 2$

Step 1

Simplify each term.

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Step 1.1

Multiply $\log (x) \cdot 20$ .

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Step 1.1.1

Reorder $\log (x)$ and $20$ .

$20 \cdot \log (x) + \log (x) \cdot 2$

Step 1.1.2

Simplify $20 \cdot \log (x)$ by moving $20$ inside the logarithm.

$\log (x^{20}) + \log (x) \cdot 2$

Step 1.2

Multiply $\log (x) \cdot 2$ .

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Step 1.2.1

Reorder $\log (x)$ and $2$ .

$\log (x^{20}) + 2 \cdot \log (x)$

Step 1.2.2

Simplify $2 \cdot \log (x)$ by moving $2$ inside the logarithm.

$\log (x^{20}) + \log (x^{2})$

Step 2

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$\log (x^{20} x^{2})$

Step 3

Multiply $x^{20}$ by $x^{2}$ by adding the exponents.

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Step 3.1

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

$\log (x^{20 + 2})$

Step 3.2

Add $20$ and $2$ .

$\log (x^{22})$