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Math Help - quick algebra solving equation problem

  1. #1
    Junior Member
    Joined
    Dec 2006
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    quick algebra solving equation problem

    please help:

    1) 275 = 150 (1+x)^16
    how do i solve for x?

    2) 500 = 100 (1+0.065/2)^n
    solve for n

    thank you
    these are compound interest problems if ur wondering.
    Last edited by checkmarks; February 9th 2007 at 03:27 PM.
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  2. #2
    MHF Contributor
    Joined
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    Quote Originally Posted by checkmarks View Post
    please help:

    1) 275 = 150 (1+x)^16
    how do i solve for x?

    2) 500 = 100 (1+0.065/2)^n
    solve for n

    thank you
    these are compound interest problems if ur wondering.
    1.) 275 = 150(1+x)^16
    275/150 = (1+x)^16
    Raise both sides to their 1/16th power,
    (275/150)^(1/16) = 1+x
    1.038610215 = 1 +x
    x = 0.038610215 ---------------answer.

    Another way, using logarithms:
    275 = 150(1+x)^16
    275/150 = (1+x)^16
    1.833333333 = (1+x)^16
    Take the natural logs of both sides, -----(use common logs if you like).
    Ln(1.8333333333) = 16Ln(1+x)
    0.606135804 = 16Ln(1+x)
    Divide both sides by 16,
    0.037883488 = Ln(1+x)
    e^0.037883488 = 1+x
    1.038610215 = 1+x
    x = 0.038610215 -----------same as above.

    --------------------------------------------------
    2) 500 = 100 (1+0.065/2)^n

    Here you'd be forced to use logarithms only.

    Divide both sides by 100,
    5 = (1.0325)^n
    Ln(5) = n*Ln(1.0325)
    n = Ln(5) / Ln(1.0325)
    n = 50.32159601 -----------------answer.
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