Question

Sobre Logaritmos !!! Agradeço!!!

Answer 1

  Bom dia

  6)

  a)

  y = log3(5) * log25(27)  
  y = log(5)/log(3) * log(27)/log(25) 
  y = 3log(3)*log(5)/(2log(3)*log(5)) = 3/2

  b)   

  y = log3(2)*log4(3)*log5(4)*log6(5)*log7(6)*log8(7)*log9(8)*log10(9) 
  y = log(2)*log(3)*log(4)*log(5)*log(6)*log(7)*log(8)*log(9)/ 
        (log(3)*log(4)*log(5)*log(6)*log(7)*log(8*log(9)*log(10)
  y = log(2)/log(10) = log(2)

  7) log(2) = a, log(3) = b  
      y = log100(72) = log(72)/log(100) = log(8*9)/2 
      y = 3log(2)/2 + 2log(3)/2   y = 3a/2 + b

  8) log(2) = 0.30, log(7) = 0.85
      log(14) = log(2*7) = log(2) + log(7) = 0.30 + 0.85 = 1.15 (D)

  9) log(3) = 0.48, log(7) = 0.84    log(21) = log(3*7) = log(3) + log(7) = 0.48 + 0.84 = 1.32 (C)   

10) 

  log2(6) + 2log2(5) = log2(6) + log2(25) = log2(6*25) = log2(150) (D)

11)

 log3(x) = log3(4),  x = 4 
 log4(2x + 10) = log4(16), 2x + 10 = 16, 2x = 6, x = 3 
 log3(x + 1) = log(-x + 3), x + 1 = -x + 3, 2x = 2, x = 1 
 log(7x - 1) = log(4x + 8),  7x - 1 = 4x + 8, 3x = 9, x = 3