Question

3 log (base2)5+log (base2)10-log (base2)625​

Answer 1

Step-by-step explanation:

$3 ( log_{2}(5) ) + log_{2}(10) - log_{2}(625) \\ \\ = log_{2}(5) {}^{3} + log_{2}(10) - log_{2}(625) \\ \\ (Formula - \: \: \: \: m( log_{a}(n) ) = log_{a}(n) {}^{m} ) \\ and \\ \\ = log_{2}( \frac{ {5}^{3} \times 10 }{625} ) \\ \\ = log_{2}( \frac{125 \times 10}{625} ) \\ \\ = log_{2}( \frac{10}{5} ) \\ \\ = log_{2}(2)$

$note \: \: \\ log(a) + log(b) = log(a \times b) \\ \\ log(a) - log(b) = log( \frac{a}{b} )$