Algebra Examples

$2 \log_{4} (20) - 2 \log_{4} (12)$

Step 1

Simplify each term.

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Step 1.1

Simplify $2 \log_{4} (20)$ by moving $2$ inside the logarithm.

$\log_{4} (20^{2}) - 2 \log_{4} (12)$

Step 1.2

Raise $20$ to the power of $2$ .

$\log_{4} (400) - 2 \log_{4} (12)$

Step 1.3

Simplify $- 2 \log_{4} (12)$ by moving $2$ inside the logarithm.

$\log_{4} (400) - \log_{4} (12^{2})$

Step 1.4

Raise $12$ to the power of $2$ .

$\log_{4} (400) - \log_{4} (144)$

Step 2

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$\log_{4} (\frac{400}{144})$

Step 3

Cancel the common factor of $400$ and $144$ .

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Step 3.1

Factor $16$ out of $400$ .

$\log_{4} (\frac{16 (25)}{144})$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $16$ out of $144$ .

$\log_{4} (\frac{16 \cdot 25}{16 \cdot 9})$

Step 3.2.2

Cancel the common factor.

$\log_{4} (\frac{16 \cdot 25}{16 \cdot 9})$

Step 3.2.3

Rewrite the expression.

$\log_{4} (\frac{25}{9})$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\log_{4} (\frac{25}{9})$

Decimal Form:

$0.73696559 \dots$