Precalculus Examples

$\log (48) - \log (16) + \log (4)$

Step 1

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

$\log (\frac{48}{16}) + \log (4)$

Step 2

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

$\log (\frac{48}{16} \cdot 4)$

Step 3

Cancel the common factor of $4$ .

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Step 3.1

Factor $4$ out of $16$ .

$\log (\frac{48}{4 (4)} \cdot 4)$

Step 3.2

Cancel the common factor.

$\log (\frac{48}{4 \cdot 4} \cdot 4)$

Step 3.3

Rewrite the expression.

$\log (\frac{48}{4})$

Step 4

Divide $48$ by $4$ .

$\log (12)$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\log (12)$

Decimal Form:

$1.07918124 \dots$