Precalculus Examples

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

Step 1

Apply the distributive property.

$\frac{1}{3} (2 \log (z)) + \frac{1}{3} (- 3 \log (x)) + \frac{1}{3} (5 \log (y))$

Step 2

Simplify.

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Step 2.1

Multiply $\frac{1}{3} (2 \log (z))$ .

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Step 2.1.1

Combine $2$ and $\frac{1}{3}$ .

$\frac{2}{3} \log (z) + \frac{1}{3} (- 3 \log (x)) + \frac{1}{3} (5 \log (y))$

Step 2.1.2

Combine $\frac{2}{3}$ and $\log (z)$ .

$\frac{2 \log (z)}{3} + \frac{1}{3} (- 3 \log (x)) + \frac{1}{3} (5 \log (y))$

Step 2.2

Cancel the common factor of $3$ .

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Step 2.2.1

Factor $3$ out of $- 3 \log (x)$ .

$\frac{2 \log (z)}{3} + \frac{1}{3} (3 (- \log (x))) + \frac{1}{3} (5 \log (y))$

Step 2.2.2

Cancel the common factor.

$\frac{2 \log (z)}{3} + \frac{1}{3} (3 (- \log (x))) + \frac{1}{3} (5 \log (y))$

Step 2.2.3

Rewrite the expression.

$\frac{2 \log (z)}{3} - \log (x) + \frac{1}{3} (5 \log (y))$

Step 2.3

Multiply $\frac{1}{3} (5 \log (y))$ .

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Step 2.3.1

Combine $5$ and $\frac{1}{3}$ .

$\frac{2 \log (z)}{3} - \log (x) + \frac{5}{3} \log (y)$

Step 2.3.2

Combine $\frac{5}{3}$ and $\log (y)$ .

$\frac{2 \log (z)}{3} - \log (x) + \frac{5 \log (y)}{3}$