1. ## 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?

2. ## 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

3. ## 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 $\displaystyle x= W(2^{10^7})$.