Precalculus Examples

$\log_{2} (\frac{x^{6} y^{7}}{8})$

Step 1

Rewrite $\log_{2} (\frac{x^{6} y^{7}}{8})$ as $\log_{2} (x^{6} y^{7}) - \log_{2} (8)$ .

$\log_{2} (x^{6} y^{7}) - \log_{2} (8)$

Step 2

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

$\log_{2} (x^{6} y^{7}) - 1 \cdot 3$

Step 3

Multiply $- 1$ by $3$ .

$\log_{2} (x^{6} y^{7}) - 3$

Step 4

Rewrite $\log_{2} (x^{6} y^{7})$ as $\log_{2} (x^{6}) + \log_{2} (y^{7})$ .

$\log_{2} (x^{6}) + \log_{2} (y^{7}) - 3$

Step 5

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

$6 \log_{2} (x) + \log_{2} (y^{7}) - 3$

Step 6

Expand $\log_{2} (y^{7})$ by moving $7$ outside the logarithm.

$6 \log_{2} (x) + 7 \log_{2} (y) - 3$