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Math Help - Exponentiating both sides of an equation.

  1. #1
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    Exponentiating both sides of an equation.

    ln(y+1)+ln(y-1)=2x+ln(x)

    So if both sides are exponentiated with base e then the resulting left side of the equation comes out to by my solutions manual:

    (y+1)*(y-1)

    I am wondering by what arithmetic or property that the "+" on the left hand side of the equation turned into a "*" or a multiplication.

    The whole equation turns out to be:

    (y+1)*(y-1)=e^(^2^x^)*x

    Thanks for any responses...
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  2. #2
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    Re: Exponentiating both sides of an equation.

    Hey sepoto.

    Basically the reason why has to do with the properties of exponentials where e^(a+b) = e^a * e^b. This is where the multiplication property comes in.
    Thanks from sepoto
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  3. #3
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    Re: Exponentiating both sides of an equation.

    I probably haven't understood your question but it gave me a chance to practice LaTeX anyway.
    Maybe it will help


    \begin{align*} \text {RHS}&=e^{2x+lnx}\\&=e^{2x}\times e^{lnx}\\&=e^{2x} \times x\\&=xe^{2x}\end{align*}
    Thanks from sepoto
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