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Math Help- Gr12

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The relation between the # of time in days, D, it takes for a planet to revolve around the Sun is related to the planer's average distance from the Sun, k, in millions of kilometres is defined by log D= 3/2logk-0.7 .

How much longer does it take Mars than
Venus to orbit the Sun if Mars is 207 million km and Venus is 108 million km away from the Sun?

The answer i got was originally 0.424.. but it seemed off to be so i tried it a different way and got 2.3 , can someone tell me which is correct?

  • Math Help- Gr12 -

    you will have to use brackets so I can tell what the order of operation is

    The way you typed it it would be

    D = (3/2)logk - 0.7
    but I have a feeling it could be
    D = 3/(2logk) - .07 or even
    D = 3/(2logk - 0.7)

  • Math Help- Gr12 -

    opps, im sorry.. its suppose to be D = (3/2)logk - 0.7

  • Math Help- Gr12 -

    so for Mars k = 207 and
    D = (3/2)log207 - .07 = 2.774

    for Venus k = 108 and
    D = (3/2)log108 - .7 = 2.350

    the difference between these two times is .4238 days, which matches appr. your first answer.

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