Question

2 - Considerando que log2 = 0,3 e lembrando que

log10 = 1, calcule o valor de log800 + log0,2.​

Answer 1

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$\boxed{\begin{array}{l}\sf \ell og800=\ell og2^5\cdot5^2\\\sf\ell og 800=5\ell og2+2\ell og5\\\sf\ell og800= 5\ell og2+2\cdot\ell og\bigg(\dfrac{10}{2}\bigg)\\\sf\ell og800=5\cdot\ell og2+2\ell og10-2\ell og2\\\sf\ell og800=5\cdot0,3+2\cdot1-2\cdot0,3\\\sf\ell og800=1,5+2-0,6=2,9\\\sf\ell og0,2=\ell og\bigg(\dfrac{10}{2}\bigg)=\ell og10-\ell og2\\\sf\ell og0,2=1-0,3=0,7\end{array}}$

$\large\boxed{\begin{array}{l}\sf \ell og 800+\ell og0,2=2,9+0,7=3,6\end{array}}$