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? asked in Science & MathematicsMathematics · 1 decade ago

evaluate log base 8 of (1/16)?

how do you solve this equation without using calculator?

4 Answers

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  • Mein Hoon Na
    Lv 7
    1 decade ago
    Favorite Answer

    we need to find

    x so that

    8^x = 1/16

    8^x = 1/16 = 16^(-1) = 4^(-2) or (2^3)^x = (2^2)^(-2)

    2^(3x) = 2^(-4)

    so 3x = - 4 or x = - 4/3

    so log base 8 of (1/16) = - 4/3

  • Anonymous
    4 years ago

    Log 8 1

    Source(s): https://shrinkurl.im/baFGW
  • Naveen Bharadwaj
    1 decade ago

    Assume base is 8 for all log here.

    log(1/16)=log1 - log 16

    =0-log16

    = - log(8*2)

    = - [ log8 + log2 ]

    = - [ 1 + log2 ]

    = - [ 1 + (1/3) ] (Because log 2= log 2/ log 8 (base is 8) = log 2/ log (2^3) = log2/3 log2 = 1/3)

    = - (4/3)

  • Davis P
    Lv 7
    1 decade ago

    8^(1/3) = 2

    16 = 2 * 8 = 8^(1/2)* 8^1 = 8^(3/2)

    log_8 (1/16) = log_8 (8^(-3/2)) = -3/2 log_8 (8) = -3/2

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