Precalculus Examples

$\log (6) + \log (8) - \log (2)$

Step 1

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

$\log (6 \cdot 8) - \log (2)$

Step 2

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

$\log (\frac{6 \cdot 8}{2})$

Step 3

Cancel the common factor of $6$ and $2$ .

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Step 3.1

Factor $2$ out of $6 \cdot 8$ .

$\log (\frac{2 (3 \cdot 8)}{2})$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $2$ out of $2$ .

$\log (\frac{2 (3 \cdot 8)}{2 (1)})$

Step 3.2.2

Cancel the common factor.

$\log (\frac{2 (3 \cdot 8)}{2 \cdot 1})$

Step 3.2.3

Rewrite the expression.

$\log (\frac{3 \cdot 8}{1})$

Step 3.2.4

Divide $3 \cdot 8$ by $1$ .

$\log (3 \cdot 8)$

Step 4

Multiply $3$ by $8$ .

$\log (24)$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\log (24)$

Decimal Form:

$1.38021124 \dots$