Precalculus Examples

$\log_{4} (16 x^{2} y)$

Step 1

Rewrite $\log_{4} (16 x^{2} y)$ as $\log_{4} (16 x^{2}) + \log_{4} (y)$ .

$\log_{4} (16 x^{2}) + \log_{4} (y)$

Step 2

Rewrite $\log_{4} (16 x^{2})$ as $\log_{4} (16) + \log_{4} (x^{2})$ .

$\log_{4} (16) + \log_{4} (x^{2}) + \log_{4} (y)$

Step 3

Expand $\log_{4} (x^{2})$ by moving $2$ outside the logarithm.

$\log_{4} (16) + 2 \log_{4} (x) + \log_{4} (y)$

Step 4

Logarithm base $4$ of $16$ is $2$ .

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