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Thread: Simple Algebra Problem

  1. #1
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    Simple Algebra Problem

    I need to solve this algebra problem for a part of a question in my Algorithms class but I have no idea how. I have access to a TI-84.

    10000*x(ln(x)/ln(2))= 1012

    How could I go about solving this? What identities can I use to simplify this? Help?
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  2. #2
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    Re: Simple Algebra Problem

    you'll need to use the calculator, can't be done by hand using elementary algebraic methods.

    note that this equation can be simplified first ...

    $\displaystyle 10^5 \cdot \frac{x\ln{x}}{\ln{2}} = 10^{12}$

    $\displaystyle \frac{x\ln{x}}{\ln{2}} = 10^7$

    now type the expression

    $\displaystyle \frac{x\ln{x}}{\ln{2}} - 10^7$

    into Y1 and use the "solver" feature to find where the equation = 0
    Thanks from sentimentGX4
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  3. #3
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    Re: Simple Algebra Problem

    This isn't an "elementary algebraic method" but from $\displaystyle \frac{x ln(x)}{ln(2)}= 10^7$ we easily get $\displaystyle xln(x)= 10^7ln(2)= ln(2^{10^7})$ and, taking the exponential of both sides $\displaystyle e^xe^{ln(x)}= xe^x= e^{ln(2^{10^7})}= 2^{10^7}$. Now, we apply the "Lambert W function" (which is defined as the inverse function to $\displaystyle f(x)= xe^x$) we have $\displaystyle x= W(2^{10^7})$.
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