Precalculus Examples

$\frac{1}{3} \cdot \log_{7} (w) + 2 \log_{7} (z) - \log_{7} (x)$

Step 1

Simplify each term.

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Step 1.1

Simplify $\frac{1}{3} \log_{7} (w)$ by moving $\frac{1}{3}$ inside the logarithm.

$\log_{7} (w^{\frac{1}{3}}) + 2 \log_{7} (z) - \log_{7} (x)$

Step 1.2

Simplify $2 \log_{7} (z)$ by moving $2$ inside the logarithm.

$\log_{7} (w^{\frac{1}{3}}) + \log_{7} (z^{2}) - \log_{7} (x)$

Step 2

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

$\log_{7} (w^{\frac{1}{3}} z^{2}) - \log_{7} (x)$

Step 3

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

$\log_{7} (\frac{w^{\frac{1}{3}} z^{2}}{x})$

Step 4

Reorder factors in $\log_{7} (\frac{w^{\frac{1}{3}} z^{2}}{x})$ .

$\log_{7} (\frac{z^{2} w^{\frac{1}{3}}}{x})$