Evaluating logarithms without a calculator

Evaluating logarithms without a calculator

Lessons

  • 1.
    Evaluate:
    a)
    log832\log_832

    b)
    log51\log_51
    [useful rule: logb1=0] \log_b1 = 0]

    c)
    log55\log_55
    [useful rule: logbb=1] \log_bb = 1]

    d)
    -3log161024 \log_{16}1024

    e)
    log3(181)\log_3 (\frac{1}{81})

    f)
    log2564 \log_2 {^5}\sqrt{64}


  • 2.
    A Logarithmic Expression As An Exponent
    Evaluate:
    a)
    3log39{3^{log_39}}
    [useful rule: blogba=a] {b^{log_ba}} = a]

    b)
    2log21024{2^{log_21024}}


  • 3.
    evaluate:
    log25125 \log_{25} \sqrt{125}

  • 4.
    without using a calculator, determine which logarithmic expression has a bigger value:
    log220 \log_220
    vs.
    log380 \log_380