To solve this equation, we can rewrite it in terms of logarithms.
[ {2}^{-x} = 16 ]
[ \log{2}({2}^{-x}) = \log{2}(16) ]
[ -x\log{2}(2) = \log{2}(16) ]
[ -x = \log_{2}(16) ]
[ x = - \log_{2}(16) ]
[ x = -\frac{\log{2}(2^{4})}{\log{2}(2)} ]
[ x = -4 ]
Therefore, the solution to the equation is [ x = -4 ]
To solve this equation, we can rewrite it in terms of logarithms.
[ {2}^{-x} = 16 ]
[ \log{2}({2}^{-x}) = \log{2}(16) ]
[ -x\log{2}(2) = \log{2}(16) ]
[ -x = \log_{2}(16) ]
[ x = - \log_{2}(16) ]
[ x = -\frac{\log{2}(2^{4})}{\log{2}(2)} ]
[ x = -4 ]
Therefore, the solution to the equation is [ x = -4 ]