Question

log da raiz de 8 com base 2

Answer 1

$log_{2}( \sqrt{8}) \ \textless \ =\ \textgreater \ log_{2}( 8^{ \frac{1}{2} } ) \ \textless \ =\ \textgreater \ { \frac{1}{2} } log_{2}(8) \ \textless \ =\ \textgreater \ { \frac{1}{2} } log_{2}( 2^{3} ) \ \textless \ =\ \textgreater \ { \frac{1}{2} }3 \ \textless \ =\ \textgreater \ { \frac{3}{2} }$

Answer 2

$\log_2( \sqrt{8})=\log_2( \sqrt{2^3} )\\ \log_2( \sqrt{8})=\log_2(2^{ \tfrac{3}{2}})\\ \log_2( \sqrt{8})=\log_2(2)^{ \tfrac{3}{2} }\\ \log_2( \sqrt{8})= \dfrac{3}{2}\cdot\log_2(2)\\\\ \log_2(2)=1,~entao..\\\\ \log_2( \sqrt{8})= \dfrac{3}{2}\cdot1\\\\ \Large\boxed{\log_2( \sqrt{8})= \dfrac{3}{2}}$