text: # What is x if log2x = log5 + log(x - 24/5) ?
  
  giorgiana1976 | College Teacher | (Level 3) Valedictorian
  
  Posted on
  
  First, we'll impose the constraints of existence of logarithms:
  
  x - 24/5>0
  
  x > 24/5
  
  2x>0
  
  x>0
  
  The common interval of admissible values for x is (24/5 ,+inf.).
  
  Now,we'll could solve the equation using the property of quotient:
  
  log 2x = log 5 - log (x - 24/5)
  
  log 2x  = log [5/(x - 24/5)]
  
  Because the bases of logarithms are matching, we'll apply the one to one property:
  
  2x = 5/(x - 24/5)
  
  We'll cross multiply;
  
  2x(x - 24/5) = 5
  
  We'll remove the brackets:
  
  2x^2 - 48x/5 - 5 = 0
  
  We'll multiply by 5:
  
  10x^2 - 48x - 25 = 0
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