Precalculus Examples

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

Step 1

Simplify each term.

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Step 1.1

Simplify $\frac{1}{5} \log_{c} (y)$ by moving $\frac{1}{5}$ inside the logarithm.

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

Step 1.2

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

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

Step 2

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

$\log_{c} (y^{\frac{1}{5}} z^{3}) - \log_{c} (x)$

Step 3

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$\log_{c} (\frac{y^{\frac{1}{5}} z^{3}}{x})$

Step 4

Reorder factors in $\log_{c} (\frac{y^{\frac{1}{5}} z^{3}}{x})$ .

$\log_{c} (\frac{z^{3} y^{\frac{1}{5}}}{x})$