Question

Determine o valor da expressão ?

Answer 1

log2 16
$log_{2}(16) \\ = log_{2}( {2}^{4} ) \\ = 4 \times log_{2}(2) \\ = 4 \times 1 = 4$
log√3 9

$log_{ \sqrt{3} }(9) \\ = log_{ {3}^{ \frac{1}{2} } }( {3}^{2} ) \\ = \frac{2}{ \frac{1}{2} } \times log_{3}(3) \\ = 4 \times 1 = 4$
log½ 4

$log_{ \frac{1}{2} }(4) \\ = log_{ {2}^{ - 1} }( {2}^{2} ) \\ = \frac{2}{ - 1} \times log_{2}(2) \\ = - 2 \times 1 \\ = - 2$
log2 16 + log√3 9 - log½ 4
= 4 + 4 - (-2)
= 4 + 4 + 2
= 10