Question

log2 = 0,3 log3 = 0,4 e Log 5 = 0,7 determine o valor de log 180​

Answer 1

$\large\boxed{\begin{array}{l}\begin{array}{c|l}\sf180&\sf2\\\sf90&\sf2\\\sf45&\sf3\\\sf15&\sf3\\\sf5&\sf5\\\sf1\end{array}\\\sf 180=2^2\cdot3^2\cdot5\\\sf \ell og(180)=\ell og(2^2\cdot3^2\cdot5)\\\sf \ell og(180)=\ell og2^2+\ell og3^2+\ell og5\\\sf \ell og(180)=2\ell og2+2\ell og3+\ell og5\\\sf \ell og(180)=2\cdot0,3+2\cdot0,4+0,7\\\sf \ell og(180)=0,6+0,8+0,7\\\sf \ell og(180)=2,1\end{array}}$