Precalculus Examples

$3 \log_{3} (y - 3 \log_{3} (z)) + 3 \log_{3} (x)$

Step 1

Simplify each term.

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Step 1.1

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

$3 \log_{3} (y - \log_{3} (z^{3})) + 3 \log_{3} (x)$

Step 1.2

Simplify $3 \log_{3} (y - \log_{3} (z^{3}))$ by moving $3$ inside the logarithm.

$\log_{3} ({(y - \log_{3} (z^{3}))}^{3}) + 3 \log_{3} (x)$

Step 1.3

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

$\log_{3} ({(y - \log_{3} (z^{3}))}^{3}) + \log_{3} (x^{3})$

Step 2

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

$\log_{3} ({(y - \log_{3} (z^{3}))}^{3} x^{3})$

Step 3

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

$\log_{3} (x^{3} {(y - \log_{3} (z^{3}))}^{3})$