Basic Math Examples

$\frac{1}{3} \log_{4} (z) + 4 \log_{4} (x) - \log_{4} (w)$

Step 1

Simplify each term.

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Step 1.1

Simplify $\frac{1}{3} \log_{4} (z)$ by moving $\frac{1}{3}$ inside the logarithm.

$\log_{4} (z^{\frac{1}{3}}) + 4 \log_{4} (x) - \log_{4} (w)$

Step 1.2

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

$\log_{4} (z^{\frac{1}{3}}) + \log_{4} (x^{4}) - \log_{4} (w)$

Step 2

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

$\log_{4} (z^{\frac{1}{3}} x^{4}) - \log_{4} (w)$

Step 3

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

$\log_{4} (\frac{z^{\frac{1}{3}} x^{4}}{w})$

Step 4

Reorder factors in $\log_{4} (\frac{z^{\frac{1}{3}} x^{4}}{w})$ .

$\log_{4} (\frac{x^{4} z^{\frac{1}{3}}}{w})$