A community for students.
Here's the question you clicked on:
 0 viewing
gerryliyana
 3 years ago
W Lambert function
gerryliyana
 3 years ago
W Lambert function

This Question is Closed

abb0t
 3 years ago
Best ResponseYou've already chosen the best response.0U ok? If it's a medical emergency, dial 911.

gerryliyana
 3 years ago
Best ResponseYou've already chosen the best response.1I want to ask u about how to derive the 3rd Equation (On picture below), becomes the4th equation (on picture below) by using WLambert function ???

abb0t
 3 years ago
Best ResponseYou've already chosen the best response.0I used to know this when I took an enzyme kinetics course and this derivation is long. About half a page  1 page typed out.

abb0t
 3 years ago
Best ResponseYou've already chosen the best response.0Maybe you can read about it on the article you found it on? http://mvputz.iqstorm.ro/upload/LogisticEnzymeKinetics_Paper1.pdf

gerryliyana
 3 years ago
Best ResponseYou've already chosen the best response.1i have been reading this paper, and I did not find what i want.., would u kindly help me?? do you still have a reference about this derivation (complete with WLambert function)

abb0t
 3 years ago
Best ResponseYou've already chosen the best response.0I will look through my notes from my kinetics class. If I find it, I'll post it.

UnkleRhaukus
 3 years ago
Best ResponseYou've already chosen the best response.1hmm , i haven't heard of the W Lambert function before

gerryliyana
 3 years ago
Best ResponseYou've already chosen the best response.1do u have any idea @oldrin.bataku ??

oldrin.bataku
 3 years ago
Best ResponseYou've already chosen the best response.2W(x) is defined such that W(x) e^W(x) = x

gerryliyana
 3 years ago
Best ResponseYou've already chosen the best response.1yes.., i know.., i did read it on wikipedia. but I'm a little bit confused how to derive it (3rd equations) :)

gerryliyana
 3 years ago
Best ResponseYou've already chosen the best response.1I'm looking for some easy derivation of the above, step by step., :)

oldrin.bataku
 3 years ago
Best ResponseYou've already chosen the best response.2$$V_{max}t=([S_0][S](t))K_M\ln\left(\frac{[S](t)}{[S_0]}\right)\\\ln\left(\frac{[S](t)}{[S_0]}\right)=\frac{[S_0][S](t)V_{max}t}{K_M}\\\frac{[S](t)}{[S_0]}=\exp\left(\frac{[S_0][S](t)V_{max}t}{K_M}\right)=\frac{e^\frac{{[S_0]V_{max}t}}{K_M}}{\frac{e^{[S](t)}}{K_M}}$$ $$[S](t)e^{[S](t)}=\frac{S_0}{K_M}e^{\frac{[S_0]V_{max}t}{K_m}}=\frac{S_0}{K_M}\exp\left(\frac{[S_0]V_{max}t}{K_m}\right)$$ $$[S](t)=W\left(\frac{S_0}{K_M}\exp\left(\frac{[S_0]V_{max}t}{K_m}\right)\right)$$

oldrin.bataku
 3 years ago
Best ResponseYou've already chosen the best response.2It's just algebra :p

abb0t
 3 years ago
Best ResponseYou've already chosen the best response.0It is just algebra :) intense algebra.

gerryliyana
 3 years ago
Best ResponseYou've already chosen the best response.1i thank all of u guys :)

gerryliyana
 3 years ago
Best ResponseYou've already chosen the best response.1thank u so much @oldrin.bataku :)

oldrin.bataku
 3 years ago
Best ResponseYou've already chosen the best response.2$$V_{max}t=([S_0][S](t))K_M\ln\left(\frac{[S](t)}{[S_0]}\right)\\\ln\left(\frac{[S](t)}{[S_0]}\right)=\frac{[S_0][S](t)V_{max}t}{K_M}\\\frac{[S](t)}{[S_0]}=\exp\left(\frac{[S_0][S](t)V_{max}t}{K_M}\right)=\frac{e^\frac{{[S_0]V_{max}t}}{K_M}}{e^\frac{[S](t)}{K_M}}$$$$\frac{[S](t)}{K_M}e^\frac{[S](t)}{K_M}=\frac{[S_0]}{K_M}e^{\frac{[S_0]V_{max}t}{K_M}}=\frac{[S_0]}{K_M}\exp\left(\frac{[S_0]V_{max}t}{K_M}\right)$$$$\frac{[S](t)}{K_M}=W\left[\frac{[S_0]}{K_M}\exp\left(\frac{[S_0]V_{max}t}{K_M}\right)\right]$$$$[S](t)=K_MW\left[\frac{[S_0]}{K_M}\exp\left(\frac{[S_0]V_{max}t}{K_M}\right)\right]$$Sorry, I made a few really dumb errors the first time! http://en.wikipedia.org/wiki/Michaelis%E2%80%93Menten_kinetics#Determination_of_constants

gerryliyana
 3 years ago
Best ResponseYou've already chosen the best response.1ok.., no problem, thank u @oldrin.bataku ;)
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.