Question

URGENTE SCR
resolva as equações abaixo sabendo que log 2=0,3 e log 5=0,4 

a)log 0,2
b)log 16
c)log \frac{1}{16}c)log161​ 
d)log \sqrt{5}d)log5​

Answer 1

a)

$log\,0,2\\\\log\,\frac{2}{10}\\\\Aplicando\;a\;propriedade:\;log\,\frac{a}{c}=log\,a-log\,c\\\\log2-log10\\\\0,3-1\\\\-0,7$

b)

$log16\\\\log2^4\\\\Utilizando\;a\;propriedade:\;log\,a^c=c.log\,a\\\\4.log2\\\\4\;.\;0,3\\\\1,2$

c)

$log\frac{1}{16}\\\\log\,16^{-1}\\\\log(2^4)^{-1}\\\\log2^{-4}\\\\-4.log2\\\\-4\;.\;0,3\\\\-1,2$

d)

$log\sqrt{5}\\\\log5^{\frac{1}{2}}\\\\\frac{1}{2}.log5\\\\\frac{1}{2}\;.\;0,4\\\\0,2$