Evaluating logarithms without a calculator

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  1. Evaluate:
    1. log832\log_832
    2. log51\log_51
      [useful rule: logb1=0] \log_b1 = 0]
    3. log55\log_55
      [useful rule: logbb=1] \log_bb = 1]
    4. -3log161024 \log_{16}1024
    5. log3(181)\log_3 (\frac{1}{81})
    6. log2564 \log_2 {^5}\sqrt{64}
  2. A Logarithmic Expression As An Exponent
    1. 3log39{3^{log_39}}
      [useful rule: blogba=a] {b^{log_ba}} = a]
    2. 2log21024{2^{log_21024}}
  3. evaluate:
    log25125 \log_{25} \sqrt{125}
    1. without using a calculator, determine which logarithmic expression has a bigger value:
      log220 \log_220
      log380 \log_380