Precalculus Examples

$\log_{a} (5) + \log_{a} (x^{3} - 2) + \log_{a} (3)$

Step 1

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

$\log_{a} (5 (x^{3} - 2)) + \log_{a} (3)$

Step 2

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

$\log_{a} (5 (x^{3} - 2) \cdot 3)$

Step 3

Apply the distributive property.

$\log_{a} ((5 x^{3} + 5 \cdot - 2) \cdot 3)$

Step 4

Multiply $5$ by $- 2$ .

$\log_{a} ((5 x^{3} - 10) \cdot 3)$

Step 5

Apply the distributive property.

$\log_{a} (5 x^{3} \cdot 3 - 10 \cdot 3)$

Step 6

Multiply.

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Step 6.1

Multiply $3$ by $5$ .

$\log_{a} (15 x^{3} - 10 \cdot 3)$

Step 6.2

Multiply $- 10$ by $3$ .

$\log_{a} (15 x^{3} - 30)$