Question

Sabendo que log2=0,3 e log3=0,48, calcule:

log de 50 na base 9

Answer 1

Log(9)50 = 
Log(3²)(5*10) = 
1/2*Log(3)5+1/2*Log(3)10 = 
1/2*Log(3)(10/2)+1/2*1/(Log(10)3) = 
1/2*Log(3)10 - Log(3)2 + 1/2*(1/0,48) = 
1/2*1/(log(10)3) - (Log 3)/(Log 2) + 1/2*(100/48) = 
1/2*1/0,48 - 0,48/0,3+1/2*(25/12) = 
1/2*100/48 - 48/3+25/24 = 
100/96-16+25/24 = 
50/48 - 16/1 + 25/24 = 
mmc (48,1,24) = 48
(48:48*50)/48 - (48:1*16)/48+(48:24*25)/48 = 
50/48 - (48*16)/48 + (2*25)/48 = 
50/48 - 3/48 + 50/48 = 
(50-3+50)/48 = 
103/48