Precalculus Examples

$5 \log_{3} (x) + 4 \log_{3} (x - 3)$

Step 1

Simplify each term.

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Step 1.1

Simplify $5 \log_{3} (x)$ by moving $5$ inside the logarithm.

$\log_{3} (x^{5}) + 4 \log_{3} (x - 3)$

Step 1.2

Simplify $4 \log_{3} (x - 3)$ by moving $4$ inside the logarithm.

$\log_{3} (x^{5}) + \log_{3} ({(x - 3)}^{4})$

Step 2

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

$\log_{3} (x^{5} {(x - 3)}^{4})$