Precalculus Examples

$\log_{7} ({(x y^{6})}^{4})$

Step 1

Expand $\log_{7} ({(x y^{6})}^{4})$ by moving $4$ outside the logarithm.

$4 \log_{7} (x y^{6})$

Step 2

Rewrite $\log_{7} (x y^{6})$ as $\log_{7} (x) + \log_{7} (y^{6})$ .

$4 (\log_{7} (x) + \log_{7} (y^{6}))$

Step 3

Expand $\log_{7} (y^{6})$ by moving $6$ outside the logarithm.

$4 (\log_{7} (x) + 6 \log_{7} (y))$

Step 4

Apply the distributive property.

$4 \log_{7} (x) + 4 (6 \log_{7} (y))$

Step 5

Multiply $6$ by $4$ .

$4 \log_{7} (x) + 24 \log_{7} (y)$