Question

URGENTE
O valor da expressão log₃27 + log₃9 + log₃3 + log₃1 corresponde a: *
2
3
4
5
6

Answer 1

$\sf log_{3}(27) + log_{ 3}(9) + log_{3}(3) + log_{3}(1)$

$\sf = log_{3}(3^{3} ) + log_{ 3}( {3}^{2} ) + 1 + 0$

$\sf = log_{3}(3^{3} ) + log_{ 3}( {3}^{2} ) + 1$

$\sf = 3log_{3}(3) + 2log_{ 3}( {3} ) + 1$

$\sf = 3\cdot 1 + 2\cdot 1+ 1$

$\sf = 3+ 2+ 1$

$\sf \red{ = 6}$