3. If (0.2)x = 2 and log 2 = 0.3010, then the value of x to the nearest tenth is:​

Question

3. If (0.2)x = 2 and log 2 = 0.3010, then the value of x to the nearest tenth is:​

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Elliana 6 months 2021-12-10T17:45:56+00:00 2 Answers 0 views 0

Answers ( )

  1. Elliana
    0
    2021-12-10T17:47:06+00:00
    Reply

    Step-by-step explanation:

    {0.2}^{x} = 2

    Applying log both sides we get

    log({0.2}^{x} ) = log(2)

    x log(0.2) = log(2)

    x log( \frac{2}{10} ) = log( {2} )

    x( log(2) - log(10) ) = log(2)

    x(0.3010 - 1) = 0.3010

    x = \frac{0.3010}{ - 0.699}

    x = - 0.4306

  2. Elliana
    0
    2021-12-10T17:47:07+00:00
    Reply

    → Solution:

    (0.2)x = 2.

    Taking log on both sides

    log (0.2)x = log 2.

    x log (0.2) = 0.3010, [since log 2 = 0.3010].

    x log (2/10) = 0.3010.

    x [log 2 – log 10] = 0.3010.

    x [log 2 – 1] = 0.3010,[since log 10=1].

    x [0.3010 -1] = 0.3010, [since log 2 = 0.3010].

    x[-0.699] = 0.3010.

    x = 0.3010/-0.699.

    x = -0.4306….

    x = -0.4 (nearest tenth)

    Answer: (c)

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