Question

Sendo log 2 = a, log 3 = b e log 5 = c, determine o valor de log 240: *
A) 3a + 2b + c
B) 4a + 2b + c
C) 4a + b + 2c
D) 4a + b + c

Answer 1

$\boxed{\begin{array}{l}\rm \ell og2=a~~\ell og3=b~~\ell og5=c\\\begin{array}{c|l}\sf240&\sf2\\\sf 120&\sf2\\\sf 60&\sf2\\\sf 30&\sf2\\\sf 15&\sf3\\\sf 5&\sf5\\\sf 1\end{array}\\\sf 240=2^4\cdot3\cdot5\\\sf \ell og240=\ell og(2^4\cdot3\cdot5)\\\sf \ell og240=\ell og2^4+\ell og3+\ell og5\\\sf\ell og240=4\ell og2+\ell og3+\ell og5\\\sf \ell og240=4a+b+c\\\huge\boxed{\boxed{\boxed{\boxed{\sf\maltese~alternativa~ D}}}}\end{array}}$