Evaluating logarithms without a calculator

All in One Place

Everything you need for better grades in university, high school and elementary.

Learn with Ease

Made in Canada with help for all provincial curriculums, so you can study in confidence.

Instant and Unlimited Help

Get the best tips, walkthroughs, and practice questions.

  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