sabendo que log de 3 na base 5 = 0,68 e log 2 na base 5 = 0,43?

arroz-dumal

qual o log de 12 na base 5?

qual o log de 54 na base 12?

Update:

no log5 12 fica:

log5 (2.2.3)

log5 2 + log5 2 + log5 3

0.43 + 0.43 + 0.68 = 1.54

não consigo fazer a segunda!

scorpion

log[5] 3 = 0,68

log[5] 2 = 0,43

= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

log[5] (12)

* fatorando 12 obtemos, 12 = 2².3

log[5] (12) = log[5] (2².3)

log[5] (12) = log[5] (2²) + log[5] (3)

log[5] (12) = 2.log[5] (2) + log[5] (3)

log[5] (12) = 2.(0,43) + (0,68)

log[5] (12) = 1,54 ( ≈ 1,544 )

= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

log[12] 54

* mudança de base...

log[12] (54) = ( log[5] (54) ) / ( log[5] (12) )

* fatorando 54 obtemos, 12 = 2.3³

* fatorando 12 obtemos, 12 = 2².3

log[12] (54) = ( log[5] (2.3³) ) / ( log[5] (2².3) )

log[12] (54) = ( log[5] (2) + log[5] (3³) ) / ( log[5] (2²) + log[5] (3) )

log[12] (54) = ( log[5] (2) + 3.log[5] (3) ) / ( 2.log[5] (2) + log[5] (3) )

log[12] (54) = ( 0,43 + 3.(0,68) ) / ( 2.(0,43) + 0,68 )

log[12] (54) = 1,60 ( ≈ 1,605 )

gmramella

log 5 3=0.68

log 5 2=0.43

log 5 12=log 5 (6+6)=log 5 6+log 5 6=log 5 (3+3)+log 5 (3+3)=4(log 5 3)

4*0.68=2.72

log b a=(log c a)/(log c b)

log 12 54=(log 5 54)/(log 5 12)=2(log 5 27)/2(log 5 6)=(log 5 27)/(log 5 6)=3(log 5 9)/3(log 5 2)=

(log 5 9)/(log 5 2)=3(log 5 3)/(log 5 2)=3(0.68)/0.43=2.04/0.43~4,7441

roxanne-wilson_60b7fe40c151c

que?