Question

Consideremos os seguintes dados: Log2 = 0,3 e Log3 = 0,48. Nessas condições, determine o valor de log 240 é:

Answer 1

Resposta:

log 240= 2,38

Explicação passo-a-passo:

㏒ 240=㏒ (24.10)=㏒ (2³.3.10)=㏒ 2³ +㏒ 3+ ㏒10=

=3.㏒ 2+㏒ 3 +㏒ 10= 3.0,3+ 0.48+ 1=2,38

Answer 2

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$\begin{array}{c|l}\sf240&\sf2\\\sf120&\sf2\\\sf60&\sf2\\\sf30&\sf2\\\sf15&\sf3\\\sf5&\sf5\\\sf1\end{array}\\\boxed{\begin{array}{l}\sf 240=2^4\cdot3\cdot5\\\sf \ell og240=\ell og(2^4\cdot3\cdot5)\\\sf \ell og240=\ell og2^4+\ell og3+\ell og5\\\sf \ell og240=4\ell og2+\ell og3+\ell og5\\\sf \ell og240=4\ell og2+\ell og3+\ell og\bigg(\dfrac{10}{2}\bigg)\\\sf \ell og240=4\ell og2+\ell og3+\ell og10-\ell og2\\\sf\ell og240=3\ell og2+\ell og3+\ell og10\end{array}}$

$\Large\boxed{\begin{array}{l}\sf\ell og240=3\cdot0,3+0,48+1\\\sf\ell og240=0,9+0,48+1\\\sf \ell og240=2,38\end{array}}$