Algebra Examples

$a = \log_{3} (40) - \log_{3} (5) + \log_{3} (2)$

Step 1

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

$a = \log_{3} (\frac{40}{5}) + \log_{3} (2)$

Step 2

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

$a = \log_{3} (\frac{40}{5} \cdot 2)$

Step 3

Divide $40$ by $5$ .

$a = \log_{3} (8 \cdot 2)$

Step 4

Multiply $8$ by $2$ .

$a = \log_{3} (16)$

Step 5

The result can be shown in multiple forms.

Exact Form:

$a = \log_{3} (16)$

Decimal Form:

$a = 2.52371901 \dots$