Evaluating logarithms without a calculator

Lessons

1. Evaluate:
   
   1. $\log_832$
      
   2. $\log_51$
      [useful rule: $\log_b1 = 0]$
      
   3. $\log_55$
      [useful rule: $\log_bb = 1]$
      
   4. -3$\log_{16}1024$
      
   5. $\log_3 (\frac{1}{81})$
      
   6. $\log_2 {^5}\sqrt{64}$
      
2. A Logarithmic Expression As An Exponent
   Evaluate:
   
   1. ${3^{log_39}}$
      [useful rule: ${b^{log_ba}} = a]$
      
   2. ${2^{log_21024}}$
      
3. evaluate:
   $\log_{25} \sqrt{125}$
   
4. without using a calculator, determine which logarithmic expression has a bigger value:
   
   $\log_220$
   vs.
   $\log_380$