Precalculus Examples

$\frac{1}{3} \cdot (\log_{4} (x - \log_{4} (y))) + 2 \log_{4} (x - 5)$

Step 1

Simplify each term.

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Step 1.1

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

$\log_{4} ({(x - \log_{4} (y))}^{\frac{1}{3}}) + 2 \log_{4} (x - 5)$

Step 1.2

Simplify $2 \log_{4} (x - 5)$ by moving $2$ inside the logarithm.

$\log_{4} ({(x - \log_{4} (y))}^{\frac{1}{3}}) + \log_{4} ({(x - 5)}^{2})$

Step 2

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

$\log_{4} ({(x - \log_{4} (y))}^{\frac{1}{3}} {(x - 5)}^{2})$