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

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

Step 3

Multiply the numerator by the reciprocal of the denominator.

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

Step 4

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

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Step 4.1

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

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

Step 4.2

Multiply $14$ by $11$ .

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

Step 4.3

Multiply $3$ by $5$ .

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

Step 5

Cancel the common factor of $22$ .

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Step 5.1

Factor $22$ out of $154$ .

$\log (\frac{22 (7)}{15} \cdot \frac{15}{22})$

Step 5.2

Cancel the common factor.

$\log (\frac{22 \cdot 7}{15} \cdot \frac{15}{22})$

Step 5.3

Rewrite the expression.

$\log (\frac{7}{15} \cdot 15)$

Step 6

Cancel the common factor of $15$ .

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Step 6.1

Cancel the common factor.

$\log (\frac{7}{15} \cdot 15)$

Step 6.2

Rewrite the expression.

$\log (7)$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\log (7)$

Decimal Form:

$0.84509804 \dots$