Precalculus Examples

$\log (14) + \frac{1}{2} \cdot \log (3) - \log (2)$

Step 1

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

$\frac{1}{2} \cdot \log (3) + \log (\frac{14}{2})$

Step 2

Simplify each term.

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Step 2.1

Simplify $\frac{1}{2} \log (3)$ by moving $\frac{1}{2}$ inside the logarithm.

$\log (3^{\frac{1}{2}}) + \log (\frac{14}{2})$

Step 2.2

Divide $14$ by $2$ .

$\log (3^{\frac{1}{2}}) + \log (7)$

Step 3

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

$\log (3^{\frac{1}{2}} \cdot 7)$

Step 4

Move $7$ to the left of $3^{\frac{1}{2}}$ .

$\log (7 \cdot 3^{\frac{1}{2}})$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\log (7 \cdot 3^{\frac{1}{2}})$

Decimal Form:

$1.08365866 \dots$