Question

the value of log64base root 2 is​

Answer 1

Step-by-step explanation:

$log_ {\sqrt{2}}64 \\ = \frac{log \: 64}{log \: \sqrt{2} }.. (by\:change\: of\: base \:law) \\ = \frac{log \: {2}^{6} }{log {2}^{ \frac{1}{2} } } \\ = \frac{6 \: log \: 2}{ \frac{1}{2} \: log \: 2} \\ = 6 \times 2 \times log_2 \: 2 \\ = 12 \times 1( \because \: log_2 \: 2 = 1) \\ = 12 \\ Thus, \: log_ {\sqrt{2}}64 = 12$