Register to reply

How to figure out answer to logarithm

by mycrafish
Tags: figure, logarithm
Share this thread:
mycrafish
#1
Mar17-12, 07:41 AM
P: 4
x*log(x)=0.1*x^2
Phys.Org News Partner Mathematics news on Phys.org
'Moral victories' might spare you from losing again
Fair cake cutting gets its own algorithm
Effort to model Facebook yields key to famous math problem (and a prize)
scurty
#2
Mar17-12, 08:07 AM
P: 392
My guess is that using Newton's Method would be the easiest. I don't see any easy way to isolate x in that equation.
NascentOxygen
#3
Mar17-12, 05:57 PM
HW Helper
Thanks
P: 5,162
Quote Quote by mycrafish View Post
x*log(x)=0.1*x^2
Is log = log10? Then I'd guess about, oh, let's see, .... 10?

HallsofIvy
#4
Mar17-12, 10:37 PM
Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,352
How to figure out answer to logarithm

First, of course, x= 0 is not a solution because log(0) is not defined. So you can divide both sides by x to get log(x)= 0.1 x. You can now write this as [itex]x= e^{0.1x}[/itex]. If you let y= -0.1x, that becomes [itex]-y/0.1= e^{-y}[/itex]. Now multiply on both sides by [itex]-0.1e^y[/itex] to get [itex]ye^y= -0.1[/itex].

Now we can take the Lambert W function of both sides:
y= -0.1x= W(-0.1) so x= -10W(-0.1)= -10(-0.111833)= 1.11833 (to six significant figures).

(The Lambert W function is defined as the inverse function to [itex]f(x)= xe^x[/itex]. It is also known as the "ProductLog" function. Mathematica evaluates that function and it can be evaluated at http://functions.wolfram.com/webMath...ame=ProductLog. That's what I used to get the value above.)


Register to reply

Related Discussions
U-Substitution, can't figure out where the answer comes from? Calculus & Beyond Homework 2
Cannot figure out how these conversion factors came about to this answer? Introductory Physics Homework 1
Simple Wave Problem, But I can't figure out the answer Introductory Physics Homework 3
I cant figure out the answer to this question Introductory Physics Homework 6