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March 28, 2017

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Calculate Directly

Log (base 4) 2 + log (base 16) 2

  • Calculus - ,

    since 16=4^2, log_4 = 2log_16
    so, converting all to base 4 logs,

    log4(2) + 1/2 log4(2)

    Since 2 = √4, log4(2) = 1/2, and we have

    1/2 + 1/2 (1/2) = 1/2 + 1/4 = 3/4



    or, looking at it another way,
    2 = √4, so log4(2) = 1/2
    2 = ∜16, so log16(2) = 1/4

    1/2 + 1/4 = 3/4

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