மடக்கை விதிகளும் பயிற்சிகளும்

மடக்கை(Logarithm)

• If a^x=N then log_aN=x
  
  Examples:
  10¹=10 => log₁₀10=1
  3¹=3 => log₃3=1
  2¹=2 => log₂2=1
  
  In General
  a¹=a => log_aa=1
  
  

• If a^x=N then log_aN=x
  
  Examples:
  10⁰=1 => log₁₀1=0
  3⁰=1 => log₃1=0
  2⁰=1 => log₂1=0
  
  In General
  a⁰=1 => log_a1=0

• If log_aN=x then a^x=N
  
  Examples:
  Log₁₀10=1 => 10¹=10
  Log₃3=1 => 3¹=3
  Log₂2=1 => 2¹=2
  
  In General
  Log_aa=1 => a¹=a
  
  If log_aN=x then a^x=N
  
  Examples:
  Log₁₀1=0 => 10⁰=1
  Log₃1=0 => 3⁰=1
  Log₂1=0 => 2⁰=1
  
  In General
  Log_a1=0 => a⁰=1
  

  
  

மடக்கை விதிகள்(Laws 0f Logarithm)

• log_a(mn) = log_am + log_an
  
  Examples:
  log₁₀(10x100) = log₁₀10 + log₁₀100
  
  log₅(125x25) = log₅125 + log₅25
  
  
  

• log_a(m/n) = log_am - log_an
  
  Examples:
  Log₁₀(100/10) = log₁₀100 - log₁₀10
  
  Log₅(125/25) = log₅125 - log₅25
  
  

• log_am^r = r log_am
  
  Examples:
  Log₁₀10⁴ = 4 log₁₀10
  
  Log₅125⁵= 5 log₅125
  

பயிற்சிகள்(Exercises)

• log₁₀1000
  =log₁₀10³
  = 3 log₁₀10
  = 3 x 1 (log₁₀10=1)
  =3
  
  

• log₁₀25 + log₁₀8 - log₁₀2
  =log₁₀(25 x 8 / 2)
  =log₁₀(100)
  =log₁₀10²
  =2 log₁₀10
  =2 x 1
  =2
  
  

• 2 log₁₀8 + 2 log₁₀5 = log₁₀4³ + log₁₀x
  log₁₀x = 2 log₁₀8 + 2 log₁₀5 - log₁₀4³
  = log₁₀8² + log₁₀5² - log₁₀4³
  =log₁₀(8² x 5²/4³)
  log₁₀x = log₁₀(25)
  x=25
  
  

• log₂4 + log₂8
  =log₂(4 x 8)
  =log₂(32)
  =log₂2⁵
  =5 x 1
  =5
  
  

• log₅20 + log₅4 – log₅16
  =log₅(20 x 4 / 16)
  =log₅(5)
  =1
  
  

• log₁₀200 + log₁₀300 – log₅60
  =log₁₀(200 x 300 / 60)
  =log₁₀(1000)
  =log₁₀(10³)
  =3 log₁₀10
  =3
  
  

• log₁₀x - log₁₀2 = log₁₀3 – log₁₀4 + 1
  log₁₀x =log₁₀2 + log₁₀3 – log₁₀4 + log₁₀10
  =log₁₀(2 x 3 x 10 /4)
  log₁₀x =log₁₀(15)
  x = 15