Question

Logaritmos exercícios ​

Answer 1

$\large\boxed{\begin{array}{l}\rm60)~\sf \ell og2=0,3~\ell og3=0,48~~ \ell og5=0,70 \\\rm a)~\sf \ell og20=\ell og(2\cdot10)=\ell og2+\ell og10\\\sf \ell og20=0,3+1=1,3\\\rm b)~\sf \ell og0,0002=\ell og(2\cdot10^{-4})=\ell og2-4\ell og10\\\sf \ell og0,0002=0,3-4=-3,7\\\rm c)~\sf \ell og30~000=\ell og(3\cdot10^4)=\ell og3+4\ell og10\\\sf \ell og30~000=0,48+4\cdot1=4,48\\\rm d)~\sf \ell og0,3=\ell og(3\cdot10^{-1})=\ell og3-\ell og10\\\sf \ell og0,3=0,48-1=-0,52\end{array}}$

$\large\boxed{\begin{array}{l}\rm e)~\sf \ell og500=\ell og(5\cdot10^2)=\ell og5+2\ell og10\\\sf \ell og500=0,7+2\cdot1=2,7\\\rm f)~\sf \ell og0,00005=\ell og(5\cdot10^{-5})=\ell og5-5\ell og10\\\sf \ell og0,00005=0,7-5=-4,30\\\rm g)~\sf \ell og18=\ell og(2\cdot 3^2)=\ell og2+2\ell og3\\\sf \ell og18=0,3+2\cdot0,48\\\sf \ell og18=0,3+0,96=0,99\\\rm h)~\sf \ell og45=\ell og(3^2\cdot5)=2\ell og3+\ell og5\\\sf \ell og45=2\cdot0,48+0,7\\\sf \ell og45=0,96+0,7=1,66\end{array}}$

$\large\boxed{\begin{array}{l}\rm i)~\sf \ell og72=\ell og(2^3\cdot3^2)=3\ell og2+2\ell og3\\\sf \ell og72=3\cdot0,3+2\cdot0,48\\\sf \ell og72=0,9+0,96=1,86\\\rm j)~\sf \ell og0,006=\ell og(2\cdot3\cdot10^{-3})\\\sf \ell og0,006=\ell og2+\ell og3-3\ell og10\\\sf \ell og0,006=0,3+0,48-3\cdot1\\\sf \ell og0,006=0,78-3=-2,22\end{array}}$

$\large\boxed{\begin{array}{l}\rm l)~\sf\ell og14,4=\ell og(144\cdot10^{-1})\\\sf \ell og14,4=\ell og(2^4\cdot3^2\cdot 10^{-1})\\\sf \ell og14,4=4\ell og2+2\ell og3-\ell og10\\\sf \ell og14,4=4\cdot0,3+2\cdot0,48-1\\\sf \ell og14,4=1,2+0,96-1\\\sf \ell og14,4=1,16\end{array}}$

$\large\boxed{\begin{array}{l}\rm m)~\sf \ell og0,08=\ell og(2^3\cdot10^{-2})\\\sf \ell og0,08=3\ell og2-2\ell og10\\\sf \ell og0,08=3\cdot0,3-2\cdot1\\\sf\ell og0,08=0,9-2=-1,1 \end{array}}$

$\large\boxed{\begin{array}{l}\rm n)~\sf\ell og7,5=\ell og(3\cdot5^2\cdot10^{-1})\\\sf \ell og7,5=\ell og3+2\ell og5-\ell og10\\\sf \ell og7,5=0,48+2\cdot0,7-1\\\sf \ell og7,5=0,88\end{array}}$

$\large\boxed{\begin{array}{l}\rm o)~\sf \ell og250=\ell og(5^2\cdot10)\\\sf \ell og250=2\ell og5+1=2\cdot0,7+1\\\sf \ell og250=2,4\end{array}}$

$\large\boxed{\begin{array}{l}\rm p)~\sf \ell og1,25=\ell og(5^3\cdot10^{-2})\\\sf \ell og1,25=3\ell og5-2\ell og10\\\sf \ell og1,25=3\cdot0,7-2\cdot1\\\sf \ell og1,25=2,1-2=0,1\end{array}}$

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$\large\boxed{\begin{array}{l}\rm 61)~\ell og2=0,3~\ell og7=0,85\\\rm a)~\sf \ell og14=\ell og(2\cdot7)=\ell og2+\ell og7\\\sf \ell og14=0,3+0,85=1,15\\\rm b)~\sf \ell og50= \ell og\bigg(\dfrac{10}{2}\cdot10\bigg)\\\\\sf \ell og50=\ell og10-\ell og2+\ell og10\\\sf \ell og50=2\ell og10-\ell og2\\\sf \ell og50=2\cdot1-0,3\\\sf \ell og50=2-0,3=1,7\end{array}}$

$\large\boxed{\begin{array}{l}\rm c)~\sf \ell og3,5=\ell og\bigg(\dfrac{7}{2}\bigg)=\ell og7-\ell og2\\\sf \ell og3,5=0,85-0,30\\\sf \ell og3,5=0,55\\\rm d)~\sf \ell og70=\ell og(7\cdot10)=\ell og7+\ell og10\\\sf \ell og70=0,85+1=1,85\end{array}}$

$\large\boxed{\begin{array}{l}\rm e)~\sf \ell og0,28=\ell og\bigg(\dfrac{2^2\cdot7}{10}\bigg)=2\ell og2+\ell og7-\ell og10\\\\\sf \ell og0,28=2\cdot0,3+0,85-1\\\sf \ell og0,28=0,6+0,85-1\\\sf \ell og0,28=0,45\\\rm f)~\sf \ell og25=\ell og\bigg(\dfrac{100}{4}\bigg)=\ell og\bigg(\dfrac{10^2}{2^2}\bigg)\\\\\sf \ell og25=2\ell og10-2\ell og2\\\sf \ell og25=2\cdot1-2\cdot0,3=2-0,6\\\sf \ell og25=1,40\end{array}}$

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