Precalculus Examples

$\log_{2} (8 x^{5} y)$

Step 1

Rewrite $\log_{2} (8 x^{5} y)$ as $\log_{2} (8 x^{5}) + \log_{2} (y)$ .

$\log_{2} (8 x^{5}) + \log_{2} (y)$

Step 2

Rewrite $\log_{2} (8 x^{5})$ as $\log_{2} (8) + \log_{2} (x^{5})$ .

$\log_{2} (8) + \log_{2} (x^{5}) + \log_{2} (y)$

Step 3

Expand $\log_{2} (x^{5})$ by moving $5$ outside the logarithm.

$\log_{2} (8) + 5 \log_{2} (x) + \log_{2} (y)$

Step 4

Logarithm base $2$ of $8$ is $3$ .

$3 + 5 \log_{2} (x) + \log_{2} (y)$