Precalculus Examples

$\log_{2} (\frac{x^{6}}{x^{5}})$

Step 1

Rewrite $\log_{2} (\frac{x^{6}}{x^{5}})$ as $\log_{2} (x^{6}) - \log_{2} (x^{5})$ .

$\log_{2} (x^{6}) - \log_{2} (x^{5})$

Step 2

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

$6 \log_{2} (x) - \log_{2} (x^{5})$

Step 3

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

$6 \log_{2} (x) - (5 \log_{2} (x))$

Step 4

Multiply $5$ by $- 1$ .

$6 \log_{2} (x) - 5 \log_{2} (x)$

Step 5

Subtract $5 \log_{2} (x)$ from $6 \log_{2} (x)$ .

$\log_{2} (x)$