Precalculus Examples

$5 \log_{4} (3 z + 1) + \frac{1}{4} \cdot \log_{4} (z + 7)$

Step 1

Simplify each term.

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Step 1.1

Simplify $5 \log_{4} (3 z + 1)$ by moving $5$ inside the logarithm.

$\log_{4} ({(3 z + 1)}^{5}) + \frac{1}{4} \cdot \log_{4} (z + 7)$

Step 1.2

Simplify $\frac{1}{4} \log_{4} (z + 7)$ by moving $\frac{1}{4}$ inside the logarithm.

$\log_{4} ({(3 z + 1)}^{5}) + \log_{4} ({(z + 7)}^{\frac{1}{4}})$

Step 2

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

$\log_{4} ({(3 z + 1)}^{5} {(z + 7)}^{\frac{1}{4}})$

Step 3

Reorder factors in $\log_{4} ({(3 z + 1)}^{5} {(z + 7)}^{\frac{1}{4}})$ .

$\log_{4} ({(z + 7)}^{\frac{1}{4}} {(3 z + 1)}^{5})$