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Math Help - logarithm2

  1. #1
    Faz
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    logarithm2

    make x the subject of the equation y=3e^2x
    write natural loarithm of x as ln(x)
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  2. #2
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    Solving for x

    Quote Originally Posted by Faz View Post
    make x the subject of the equation y=3e^2x
    write natural loarithm of x as ln(x)
    If you want to solve for x, you should start by taking the natural log of both sides to get:

    ln(y) = ln(3e^(2x))
    ln(y) = ln(3) + ln(e^(2x)) Used this law: ln(XY) = ln(X) + ln(Y)
    ln(y) = ln(3) + 2x*ln(e) Used this law: ln(X^y) = yln(X)

    We know that ln(e) = 1, so equation can be rewritten:
    ln(y) = ln(3) + 2x
    ln(y) - ln(3) = 2x
    ln(y/3) = 2x Used this law: ln(X/Y) = ln(X) - ln(Y)
    Solve for x:

    x = (1/2)*[ln(y/3)]

    I consulted this website for the laws that were used to simplify the equation:

    Exponents and Logarithms

    Hope this helps
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