Precalculus Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Multiply $4 (\log_{3} (x) x)$ .

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Step 1.3.1

Reorder $\log_{3} (x)$ and $4$ .

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

Step 1.3.2

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

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

Step 1.4

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

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Step 1.4.1

Multiply $- 1$ by $4$ .

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

Step 1.4.2

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

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

Step 1.4.3

Simplify $- 4 \cdot \log_{3} (x^{5})$ by moving $4$ inside the logarithm.

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

Step 1.5

Multiply the exponents in ${(x^{5})}^{4}$ .

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Step 1.5.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Step 1.5.2

Multiply $5$ by $4$ .

$\log_{3} (x^{4}) x - \log_{3} (x^{20}) w + 3 \log_{3} (z)$

Step 1.6

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

$\log_{3} (x^{4}) x - \log_{3} (x^{20}) w + \log_{3} (z^{3})$

Step 2

Reorder factors in $\log_{3} (x^{4}) x - \log_{3} (x^{20}) w + \log_{3} (z^{3})$ .

$x \log_{3} (x^{4}) - w \log_{3} (x^{20}) + \log_{3} (z^{3})$