Precalculus Examples

$\log (3) + \log (5) + \log (2) - \log (15)$

Step 1

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

$\log (3 \cdot 5) + \log (2) - \log (15)$

Step 2

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

$\log (3 \cdot 5 \cdot 2) - \log (15)$

Step 3

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

$\log (\frac{3 \cdot 5 \cdot 2}{15})$

Step 4

Cancel the common factor of $3$ and $15$ .

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Step 4.1

Factor $3$ out of $3 \cdot 5 \cdot 2$ .

$\log (\frac{3 (5 \cdot 2)}{15})$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $3$ out of $15$ .

$\log (\frac{3 (5 \cdot 2)}{3 \cdot 5})$

Step 4.2.2

Cancel the common factor.

$\log (\frac{3 (5 \cdot 2)}{3 \cdot 5})$

Step 4.2.3

Rewrite the expression.

$\log (\frac{5 \cdot 2}{5})$

Step 5

Cancel the common factor of $5$ .

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Step 5.1

Cancel the common factor.

$\log (\frac{5 \cdot 2}{5})$

Step 5.2

Divide $2$ by $1$ .

$\log (2)$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\log (2)$

Decimal Form:

$0.30102999 \dots$