Precalculus Examples

$6 \log_{6} (3 y + 1) + \frac{1}{4} \cdot \log_{6} (y + 2)$

Step 1

Simplify each term.

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Step 1.1

Simplify $6 \log_{6} (3 y + 1)$ by moving $6$ inside the logarithm.

$\log_{6} ({(3 y + 1)}^{6}) + \frac{1}{4} \cdot \log_{6} (y + 2)$

Step 1.2

Simplify $\frac{1}{4} \log_{6} (y + 2)$ by moving $\frac{1}{4}$ inside the logarithm.

$\log_{6} ({(3 y + 1)}^{6}) + \log_{6} ({(y + 2)}^{\frac{1}{4}})$

Step 2

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

$\log_{6} ({(3 y + 1)}^{6} {(y + 2)}^{\frac{1}{4}})$

Step 3

Reorder factors in $\log_{6} ({(3 y + 1)}^{6} {(y + 2)}^{\frac{1}{4}})$ .

$\log_{6} ({(y + 2)}^{\frac{1}{4}} {(3 y + 1)}^{6})$