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Math Help - Find n in an equation

  1. #1
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    Find n in an equation

    Question 1:
    A computer analysis shows that the number
    n of electronic components a company should produce for supply to equal demand is found by solving the
    equation

    (n^2) /
    500000 = 144 - (n/500)


    Find
    n.



    Question 2:
    Solve the equation ln 128 -
    3 ln(x^2) = ln 2.
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  2. #2
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    Quote Originally Posted by fyremelody View Post
    Question 1:
    A computer analysis shows that the number
    n of electronic components a company should produce for supply to equal demand is found by solving the
    equation

    (n^2) /
    500000 = 144 - (n/500)


    Find
    n.



    Question 2:
    Solve the equation ln 128 -
    3 ln(x^2) = ln 2.
    "/" is standard notation for division - x/500 is an acceptable way of saying "x divided by 500"

    n^2 = 5 \times 10^4 \left(144- \frac{n}{500}\right) = 7.2 \times 10^6 - 100n

    This is equal to n^2 + 100n  - 7.2 \times 10^6 = 0 and since it's a quadratic use the ol' quadratic formula to solve


    ----------------------------

    128 = 2^7

    Use the laws of logs to solve this one as well as the hint above

    \ln (2^7) - \ln (x^6) = \ln \left(\frac{2^7}{x^6}\right) = \left 2

    \left(\frac{2^7}{x^6}\right) = 2
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