Find the Exact Value log base 2 of 2^4- log base 2 of 2^10

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

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

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

Reduce the expression $\frac{2^{4}}{2^{10}}$ by cancelling the common factors.

Multiply by $1$ .

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

Factor $2^{4}$ out of $2^{10}$ .

$\log_{2} (\frac{2^{4} \cdot 1}{2^{4} \cdot 2^{6}})$

Cancel the common factor.

$\log_{2} (\frac{2^{4} \cdot 1}{2^{4} \cdot 2^{6}})$

Rewrite the expression.

$\log_{2} (\frac{1}{2^{6}})$

Move $2^{6}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

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

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

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

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

$- 6 \cdot 1$

Multiply $- 6$ by $1$ .

$- 6$