Precalculus Examples

$\log_{6} (x^{2} \cdot y) \cdot 2$

Step 1

Rewrite $\log_{6} (x^{2} \cdot y)$ as $\log_{6} (x^{2}) + \log_{6} (y)$ .

$(\log_{6} (x^{2}) + \log_{6} (y)) \cdot 2$

Step 2

Expand $\log_{6} (x^{2})$ by moving $2$ outside the logarithm.

$(2 \log_{6} (x) + \log_{6} (y)) \cdot 2$

Step 3

Apply the distributive property.

$2 \log_{6} (x) \cdot 2 + \log_{6} (y) \cdot 2$

Step 4

Multiply $2$ by $2$ .

$4 \log_{6} (x) + \log_{6} (y) \cdot 2$

Step 5

Move $2$ to the left of $\log_{6} (y)$ .

$4 \log_{6} (x) + 2 \log_{6} (y)$