How to figure out answer to logarithm

by mycrafish
Tags: figure, logarithm
mycrafish is offline
Mar17-12, 07:41 AM
P: 4
Phys.Org News Partner Mathematics news on
Math modeling handbook now available
Hyperbolic homogeneous polynomials, oh my!
Researchers help Boston Marathon organizers plan for 2014 race
scurty is offline
Mar17-12, 08:07 AM
P: 380
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 is offline
Mar17-12, 05:57 PM
HW Helper
P: 4,716
Quote Quote by mycrafish View Post
Is log = log10? Then I'd guess about, oh, let's see, .... 10?

HallsofIvy is offline
Mar17-12, 10:37 PM
Sci Advisor
PF Gold
P: 38,900

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 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