Precalculus Examples

$5 \log_{3} (x) - 3 \log_{3} (9) + \frac{1}{2} \cdot \log_{3} (y)$

Step 1

Simplify each term.

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Step 1.1

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

$\log_{3} (x^{5}) - 3 \log_{3} (9) + \frac{1}{2} \cdot \log_{3} (y)$

Step 1.2

Logarithm base $3$ of $9$ is $2$ .

$\log_{3} (x^{5}) - 3 \cdot 2 + \frac{1}{2} \cdot \log_{3} (y)$

Step 1.3

Multiply $- 3$ by $2$ .

$\log_{3} (x^{5}) - 6 + \frac{1}{2} \cdot \log_{3} (y)$

Step 1.4

Simplify $\frac{1}{2} \log_{3} (y)$ by moving $\frac{1}{2}$ inside the logarithm.

$\log_{3} (x^{5}) - 6 + \log_{3} (y^{\frac{1}{2}})$

Step 2

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

$\log_{3} (x^{5} y^{\frac{1}{2}}) - 6$