# Simple Algebra Problem

• Sep 16th 2012, 01:56 PM
sentimentGX4
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?
• Sep 16th 2012, 02:05 PM
skeeter
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 ...

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

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

now type the expression

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

into Y1 and use the "solver" feature to find where the equation = 0
• Sep 16th 2012, 02:32 PM
HallsofIvy
Re: Simple Algebra Problem
This isn't an "elementary algebraic method" but from $\frac{x ln(x)}{ln(2)}= 10^7$ we easily get $xln(x)= 10^7ln(2)= ln(2^{10^7})$ and, taking the exponential of both sides $e^xe^{ln(x)}= xe^x= e^{ln(2^{10^7})}= 2^{10^7}$. Now, we apply the "Lambert W function" (which is defined as the inverse function to $f(x)= xe^x$) we have $x= W(2^{10^7})$.