Use the equation and type the ordered-pairs. y = log 3 x {(1/3, a0), (1, a1), (3, a2), (9, a3), (27, a4), (81, a5)

Question

Use the equation and type the ordered-pairs. y = log 3 x {(1/3, a0), (1, a1), (3, a2), (9, a3), (27, a4), (81, a5)

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Jade 3 weeks 2022-01-06T04:37:51+00:00 1 Answer 0 views 0

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    2022-01-06T04:39:13+00:00

    Answer:

    Considering the given equation y = log_{3}x\\

    And the ordered pairs in the format (x, y)

    I don’t know if it is log of base 3 or 10, but I will assume it is 3.

    For (\frac{1}{3}, a_{0} )

    x=\frac{1}{3}

    y=a_{0}

    y = log_{3}x\\y = log_{3}(\frac{1}{3} )\\y=-\log _3\left(3\right)\\y=-1

    So the ordered pair will be (\frac{1}{3}, -1 )

    For (1, a_{1} )

    x=1

    y=a_{1}

    y = log_{3}x\\y = log_{3}1\\y = log_{3}(1)\\Note: \log _a(1)=0\\y = 0

    So the ordered pair will be (1, 0 )

    For (3, a_{2} )

    x=3

    y=a_{2}

    y = log_{3}x\\y = log_{3}3\\y = 1

    So the ordered pair will be (3, 1 )

    For (9, a_{3} )

    x=9

    y=a_{3}

    y = log_{3}x\\y = log_{3}9\\y=2\log _3\left(3\right)\\y=2

    So the ordered pair will be (9, 2 )

    For (27, a_{4} )

    x=27

    y=a_{4}

    y = log_{3}x\\y = log_{3}27\\y=3\log _3\left(3\right)\\y=3

    So the ordered pair will be (27, 3 )

    For (81, a_{5} )

    x=81

    y=a_{5}

    y = log_{3}x\\y = log_{3}81\\y=4\log _3\left(3\right)\\y=4

    So the ordered pair will be (81, 4 )

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