Question

what is value of log 16 to the base 0.5 plz answer with steps

Answer 1

$log_{0.5}(16) \\ = log_{ \frac{1}{2} }( {2}^{4} ) \\ use \: property \\ log( {a}^{m} ) = m log(a) \\ = 4 \: log_{ \frac{1}{2} }(2) \\ = 4log_{ \frac{1}{2} }( { \frac{1}{2} }^{ - 1} ) \\ = 4( - 1) log_{ \frac{1}{2} }( \frac{1}{2} ) \\ = - 4$
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