Precalculus Examples

$\log (\frac{14}{3}) + \log (\frac{11}{5}) + \log (\frac{22}{15})$

Step 1

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

$\log (\frac{14}{3} \cdot \frac{11}{5}) + \log (\frac{22}{15})$

Step 2

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

$\log (\frac{14}{3} \cdot \frac{11}{5} \frac{22}{15})$

Step 3

Multiply $\frac{14}{3} \cdot \frac{11}{5}$ .

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Step 3.1

Multiply $\frac{14}{3}$ by $\frac{11}{5}$ .

$\log (\frac{14 \cdot 11}{3 \cdot 5} \cdot \frac{22}{15})$

Step 3.2

Multiply $14$ by $11$ .

$\log (\frac{154}{3 \cdot 5} \cdot \frac{22}{15})$

Step 3.3

Multiply $3$ by $5$ .

$\log (\frac{154}{15} \cdot \frac{22}{15})$

Step 4

Multiply $\frac{154}{15} \cdot \frac{22}{15}$ .

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Step 4.1

Multiply $\frac{154}{15}$ by $\frac{22}{15}$ .

$\log (\frac{154 \cdot 22}{15 \cdot 15})$

Step 4.2

Multiply $154$ by $22$ .

$\log (\frac{3388}{15 \cdot 15})$

Step 4.3

Multiply $15$ by $15$ .

$\log (\frac{3388}{225})$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\log (\frac{3388}{225})$

Decimal Form:

$1.17776088 \dots$