Evaluating logarithms without a calculator

Lessons

• 1.
  Evaluate:
  
  a)

  $\log_832$
  
  
  
  b)

  $\log_51$

  [useful rule: $\log_b1 = 0]$
  
  
  
  c)

  $\log_55$

  [useful rule: $\log_bb = 1]$
  
  
  
  d)

  -3$\log_{16}1024$
  
  
  
  e)

  $\log_3 (\frac{1}{81})$
  
  
  
  f)

  $\log_2 {^5}\sqrt{64}$
  
  
  

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• 2.
  A Logarithmic Expression As An Exponent
  Evaluate:
  
  a)

  ${3^{log_39}}$

  [useful rule: ${b^{log_ba}} = a]$
  
  
  
  b)

  ${2^{log_21024}}$
  
  
  

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• 3.
  evaluate:

  $\log_{25} \sqrt{125}$
  

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• 4.
  without using a calculator, determine which logarithmic expression has a bigger value:
  

  $\log_220$

  vs.

  $\log_380$

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