Precalculus Examples

$\log_{3} (80 x) - 2 + \log_{3} (x^{2} - 1)$

Step 1

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

$\log_{3} (80 x (x^{2} - 1)) - 2$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$\log_{3} (80 x \cdot x^{2} + 80 x \cdot - 1) - 2$

Step 2.2

Multiply $x$ by $x^{2}$ by adding the exponents.

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Step 2.2.1

Move $x^{2}$ .

$\log_{3} (80 (x^{2} x) + 80 x \cdot - 1) - 2$

Step 2.2.2

Multiply $x^{2}$ by $x$ .

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Step 2.2.2.1

Raise $x$ to the power of $1$ .

$\log_{3} (80 (x^{2} x^{1}) + 80 x \cdot - 1) - 2$

Step 2.2.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\log_{3} (80 x^{2 + 1} + 80 x \cdot - 1) - 2$

Step 2.2.3

Add $2$ and $1$ .

$\log_{3} (80 x^{3} + 80 x \cdot - 1) - 2$

Step 2.3

Multiply $- 1$ by $80$ .

$\log_{3} (80 x^{3} - 80 x) - 2$