text: # What is the solution of the equation log15 [1/(3^x + x - 5)]=x*(log15 5 - 1) ?
  
  We have to solve log(15) [1/(3^x + x - 5)] = x * (log(15) 5 - 1).
  
  log(15) [1/(3^x + x - 5)] = x * (log(15) 5 - 1)
  
  => log(15) [1/(3^x + x - 5)] = x*log(15) 5 - x
  
  => log(15) [1/(3^x + x - 5)] = x*log(15) 5 - log (15) 15^x
  
  => log(15) [1/(3^x + x - 5)] = log(15) (5^x/ 15^x)
  
  => [1/(3^x + x - 5)] = 5^x/ 15^x
  
  => [1/(3^x + x - 5)] = 1/ 3^x
  
  => 3^x = 3^x + x - 5
  
  => x - 5 = 0
  
  => x = 5
  
  We get x = 5
  
  Approved by eNotes Editorial Team
  
  Posted on