Trigonometry Examples

$\log (\frac{75}{16}) + \log (\frac{32}{243})$

Step 1

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

$\log (\frac{75}{16} \cdot \frac{32}{243})$

Step 2

Cancel the common factor of $3$ .

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Step 2.1

Factor $3$ out of $75$ .

$\log (\frac{3 (25)}{16} \cdot \frac{32}{243})$

Step 2.2

Factor $3$ out of $243$ .

$\log (\frac{3 \cdot 25}{16} \cdot \frac{32}{3 \cdot 81})$

Step 2.3

Cancel the common factor.

$\log (\frac{3 \cdot 25}{16} \cdot \frac{32}{3 \cdot 81})$

Step 2.4

Rewrite the expression.

$\log (\frac{25}{16} \cdot \frac{32}{81})$

Step 3

Cancel the common factor of $16$ .

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Step 3.1

Factor $16$ out of $32$ .

$\log (\frac{25}{16} \cdot \frac{16 (2)}{81})$

Step 3.2

Cancel the common factor.

$\log (\frac{25}{16} \cdot \frac{16 \cdot 2}{81})$

Step 3.3

Rewrite the expression.

$\log (25 (\frac{2}{81}))$

Step 4

Combine $25$ and $\frac{2}{81}$ .

$\log (\frac{25 \cdot 2}{81})$

Step 5

Multiply $25$ by $2$ .

$\log (\frac{50}{81})$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\log (\frac{50}{81})$

Decimal Form:

$- 0.20951501 \dots$