Question

sendo log de 2 = 0,3 é log de 3 = 0,4 log de 5 = 0,7 calcule log de 50 na base 2? heeelllpppp :)

Answer 1

Fatorando o 50, teremos: 50 = 2.5²
log₂50 = log₂(2.5²) =  log₂2 +  log₂5²
log₂50 = log₂2 + 2.log₂5
log₂50 = 1 + 2.(log 5/log2)
log₂50 = 1 + 2.(0,7/0,3)
log₂50 = 1 + 2.$(\frac{ \frac{7}{10}}{ \frac{3}{10} } )$
log₂50 = 1 + 2.$( \frac{7}{10}. \frac{10}{3})$
log₂50 = 1 + 2.(7/3)
log₂50 = 1 + 14/3
log₂50 = $\frac{3+ 14}{3}$
log₂50 = 17/3 ≈ 5,7 (aproximadamente)