Math Help Please!?

Update:

Answer Choices:

3.96 bits

3.06 bits

4.26 bits

2.64 bits

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1 Answer

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  • log[2](1/0.16)

    log[2](0.16^(-1))

    -1 * log[2](0.16)

    -1 * log[2](16/100)

    -1 * log[2](16) + log[2](100)

    log[2](100) - log[2](16)

    log[2](100) - 4

    log[2](100) =>

    2 * log[2](10) =>

    2 * log(10) / log(2)

    log(2) = 0.301, roughly

    2 * 1 / 0.301

    2/0.301

    2000/301

    301 * 6 = 1806

    2000 - 1806 = 194

    6 + 194/301 - 4 =>

    2 + 194/301

    301 is pretty close to 300, so we can approximate a little more

    2 + 194/300

    2 + 1.94/3

    2 + 0.646666666666....

    2.64

    Or we could just use a calculator

    log[2](1 / 0.16) =>

    log(0.16^(-1)) / log(2) =>

    -1 * log(0.16) / log(2) =>

    ‭2.6438561897747246957406388589788‬

    2.64

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