Precalculus Examples

$3 (\log_{4} (z - 4 \log_{4} (y)) + 2 \log_{4} (x))$

Step 1

Simplify each term.

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Step 1.1

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

$3 (\log_{4} (z - \log_{4} (y^{4})) + 2 \log_{4} (x))$

Step 1.2

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

$3 (\log_{4} (z - \log_{4} (y^{4})) + \log_{4} (x^{2}))$

Step 2

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

$3 \log_{4} ((z - \log_{4} (y^{4})) x^{2})$

Step 3

Apply the distributive property.

$3 \log_{4} (z x^{2} - \log_{4} (y^{4}) x^{2})$

Step 4

Simplify $3 \log_{4} (z x^{2} - \log_{4} (y^{4}) x^{2})$ by moving $3$ inside the logarithm.

$\log_{4} ({(z x^{2} - \log_{4} (y^{4}) x^{2})}^{3})$

Step 5

Reorder factors in $\log_{4} ({(z x^{2} - \log_{4} (y^{4}) x^{2})}^{3})$ .

$\log_{4} ({(z x^{2} - x^{2} \log_{4} (y^{4}))}^{3})$