Trigonometry Examples

$\frac{\log (11)}{3} + \frac{\log (5)}{3} + \frac{\log (2)}{3}$

Step 1

Combine the numerators over the common denominator.

$\frac{\log (11) + \log (5) + \log (2)}{3}$

Step 2

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

$\frac{\log (11 \cdot 5) + \log (2)}{3}$

Step 3

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

$\frac{\log (11 \cdot 5 \cdot 2)}{3}$

Step 4

Multiply $11 \cdot 5 \cdot 2$ .

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Step 4.1

Multiply $11$ by $5$ .

$\frac{\log (55 \cdot 2)}{3}$

Step 4.2

Multiply $55$ by $2$ .

$\frac{\log (110)}{3}$

Step 5

Rewrite $\frac{\log (110)}{3}$ as $\frac{1}{3} \log (110)$ .

$\frac{1}{3} \log (110)$

Step 6

Simplify $\frac{1}{3} \log (110)$ by moving $\frac{1}{3}$ inside the logarithm.

$\log (110^{\frac{1}{3}})$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\log (110^{\frac{1}{3}})$

Decimal Form:

$0.68046422 \dots$