Question

Qual o log de 12 na base 5, onde log 2 é 0.301 log 3 é 0.477 log 5 é 0.699??

Answer 1

$log_{_5}12\\\\Utilizando\;a\;propriedade\;de\;troca\;de\;base:\\\\log_{_5}12=\frac{log_{_{10}}12}{log_{_{10}}5}\\\\\\log_{_5}12=\frac{log_{_{10}}(2\,.\,2\,.\,3)}{log_{_{10}}5}\\\\Utilizando \;a\; propriedade:\;log\,(a\,.\,c)=log\,a+log\,c\\\\log_{_5}12=\frac{log_{_{10}}2\,+\,log_{_{10}}2\,+\,log_{_{10}}3}{log_{_{10}}5}\\\\\\log_{_5}12=\frac{0,301+0,301+0,477}{0,699}\\\\\\log_{_5}12=\frac{1,079}{0,699}\\\\\\log_{_5}12=1,544$