Question

dados log2=a e log 3 =b,determine o valor do log 600​

Answer 1

$\large\boxed{\begin{array}{l}\begin{array}{c|l}\sf600&\sf2\\\sf300&\sf2\\\sf150&\sf2\\\sf75&\sf3\\\sf25&\sf5\\\sf5&\sf5\\\sf1\end{array}\\\sf 600=2^3\cdot3\cdot5^2\\\sf \ell og(600)=\ell og(2^3\cdot3\cdot5^2)\\\sf\ell og(600)=\ell og2^3+\ell og3+\ell og5^2\\\sf \ell og(600)=3\ell og2+\ell og3+2\ell og5\\\sf \ell og5=\ell og\bigg(\dfrac{10}{2}\bigg)=\ell og10-\ell og2=1-a\\\sf \ell og(600)=3a+b+2\cdot(1-a)\\\sf \ell og(600)=3a+b+2-2a\\\sf\ell og(600)=a+b+2\end{array}}$