4) Use properties of logarithms to evaluate the expression. \( \log _{2} 160-\log _{2} 5 \)

To evaluate the expression \( \log_{2} 160 - \log_{2} 5 \), we can use the property of logarithms that states \( \log_{b} a - \log_{b} c = \log_{b} \left(\frac{a}{c}\right) \). So, we rewrite the expression as: \[ \log_{2} \left( \frac{160}{5} \right) \] Calculating the division gives us \( \frac{160}{5} = 32 \). Therefore, our expression simplifies to: \[ \log_{2} 32 \] Since \( 32 \) is \( 2^5 \), we can simplify further: \[ \log_{2} 32 = \log_{2} (2^5) = 5 \] Thus, \( \log_{2} 160 - \log_{2} 5 = 5 \).