Find the logarithm. \( \log _{2}\left(\frac{1}{16}\right)=\square \)

To solve \( \log _{2}\left(\frac{1}{16}\right) \), we can rewrite \( \frac{1}{16} \) as \( 16^{-1} \). Now, since \( 16 = 2^4 \), we have: \[ \frac{1}{16} = 16^{-1} = (2^4)^{-1} = 2^{-4} \] Now we can express the logarithm: \[ \log_{2}\left(\frac{1}{16}\right) = \log_{2}(2^{-4}) \] Using the property of logarithms that states \( \log_b(b^x) = x \): \[ \log_{2}(2^{-4}) = -4 \] Thus, \[ \log_{2}\left(\frac{1}{16}\right) = -4. \]