Question

sabendo se que log2=0,30 e log3 = 0,48,calcule o log. a)0,12 b)0,15 c)0,18 d)0,20 e)0,32

Answer 1

a)

$0,12=\frac{2*2*3}{100}=\frac{2*2*3}{10^2} \\\\log\;0,12=log\;\frac{2*2*3}{10^2}\\\\(log\,2+log\,2+log\,3)-log\,10^2\\\\(log\,2+log\,2+log\,3)-2.log\,10\\\\\frac{0,30+0,30+0,48}{2*1}\\ \\-0,92$

b)

$0,15=\frac{3*5}{100}= \frac{3*\frac{10}{2}}{10^2} \\\\log\,0,15=log\,\frac{3*\frac{10}{2}}{10^2}\\\\\left(log\,3+(log\,10-log\,2)\right)-(log\,10^2)\\\\\left(log\,3+(log\,10-log\,2)\right)-(2.log\,10)\\\\(0,48+(1-0,30))-(2*1)\\\\0,48+0,7-2\\\\-0,82$

c)

$0,18=\frac{3*3*2}{10^2}\\ \\log\,0,18=log\,\frac{3*3*2}{10^2}\\\\log3+log3+log2-2log10\\\\-0,74$

d)

$0,20=\frac{2*2*\frac{10}{2}}{10^2} \\\\log\,0,20=log\,\frac{2*2*\frac{10}{2}}{10^2}\\\\log2+log2+(log10-log2)-2log10\\\\-0,7$

e)

$0,32=\frac{2*2*2*2*2}{10^2}\\\\log\,0,32=log\,\frac{2*2*2*2*2}{10^2}\\\\log\,2^5-log\,10^2\\\\5.log2-2log10\\\\-0,5$