Precalculus Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

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

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

Step 2

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

$\log_{3} (y^{\frac{1}{2}} x^{2}) - \log (\log_{3} (z))$

Step 3

Reorder factors in $\log_{3} (y^{\frac{1}{2}} x^{2}) - \log (\log_{3} (z))$ .

$\log_{3} (x^{2} y^{\frac{1}{2}}) - \log (\log_{3} (z))$