• Matéria: Matemática
  • Autor: ju211
  • Perguntado 9 anos atrás

log da raiz de 8 com base 2

Respostas

respondido por: mitacla
2
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} }
respondido por: korvo
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}}
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