Question

sabendo, que log de 2 = 0,3 e log 3= 0.4 calcule usando as propriedades.

Answer 1

$a)\\log\;6\\\\log\;(2\;.\;3)\\\\log2 + log3\\\\0,3+0,4\\\\0,7$

$b)\\log\;\frac{9}{8}\\\\log9-log8\\\\log3^2-log2^3\\\\2.log3-3.log2\\\\2.(0,4) - 3.(0,3)\\\\0,8 - 0,9\\\\-0,1$

$c)\\log\;1,5\\\\log\;\frac{15}{10}\\\\log\;\frac{3\;.\;5}{10}\\\\log\;\frac{3\;.\;\frac{10}{2}}{10}\\\\\left(log3 + (log10 - log2)\right)-log10\\\\\left(0,4 + (1 - 0,3)\right)-1\\\\(0,4+ 0,7)-1\\\\1,1-1\\\\0,1$

$d)\\log_{_3}30\\\\log_{_3}(3\;.\;10)\\\\log_{_3}3+log_{_3}10\\\\Utilizando\;a\;mudanca\;de\;base\;no\;segundo\;log\\\\log_{_3}3+\frac{log_{_{10}}10}{log_{_{10^}}3}}\\\\1+\frac{1}{0,4}\\\\1+\frac{10}{4}\\\\1+2,5\\\\3,5$