Expand the Logarithmic Expression log base 2 of (2^4)/(2^10)

$\log_{2} (\frac{2^{4}}{2^{10}})$

Step 1

Rewrite $\log_{2} (\frac{2^{4}}{2^{10}})$ as $\log_{2} (2^{4}) - \log_{2} (2^{10})$ .

$\log_{2} (2^{4}) - \log_{2} (2^{10})$

Step 2

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

$4 \log_{2} (2) - \log_{2} (2^{10})$

Step 3

Expand $\log_{2} (2^{10})$ by moving $10$ outside the logarithm.

$4 \log_{2} (2) - (10 \log_{2} (2))$

Step 4

Logarithm base $2$ of $2$ is $1$ .

$4 \cdot 1 - (10 \log_{2} (2))$

Step 5

Logarithm base $2$ of $2$ is $1$ .

$4 \cdot 1 - (10 \cdot 1)$

Step 6

Multiply $4$ by $1$ .

$4 - (10 \cdot 1)$

Step 7

Multiply $10$ by $1$ .

$4 - 1 \cdot 10$

Step 8

Multiply $- 1$ by $10$ .

$4 - 10$

Step 9

Subtract $10$ from $4$ .

$- 6$