Solving for X with Ln

[ja100]

Hi
It has been a long time since I solved a natural logarithmic problem. So here goes. Will really appreciate a step by step solution to the problem. Solving for X
17.1=-72(0.21X*X+ ln(1-x))

 

[Dr.Peterson]

Do you mean, [MATH]17.1 = -72(0.21x^2 + \ln(1-x))[/MATH]?

This kind of equation, with the variable both inside and outside a logarithm, typically can't be solved algebraically. It can, on the other hand, be solved numerically (e.g. with a graphing calculator or equivalent); the answer is about 0.2193. (See here.)

Can you tell us the context of the question, and why you think it should be solvable? (Or is it acceptable to solve it by other means, obtaining an approximate solution as I did?)

 

[ja100]

Do you mean, [MATH]17.1 = -72(0.21x^2 + \ln(1-x))[/MATH]?

This kind of equation, with the variable both inside and outside a logarithm, typically can't be solved algebraically. It can, on the other hand, be solved numerically (e.g. with a graphing calculator or equivalent); the answer is about 0.2193. (See here.)

Can you tell us the context of the question, and why you think it should be solvable? (Or is it acceptable to solve it by other means, obtaining an approximate solution as I did?)

The value seems about right but how did you reach this point. Can you elaborate step by step?
Hydrates are formed in Petroleum systems at low temperature. X is the molar weight of hydrate inhibitors. And T is the dissociation temperature.

 

[Dr.Peterson]

I used Desmos to graph each side and show the intersection; and (as I showed you) I used Wolfram Alpha, which used whatever numerical method it chose (and shows the same graph).

What kind of answer do you need (as opposed to wish for)? If WA didn't give a formula, I can't either.

 

[ja100]

I used Desmos to graph each side and show the intersection; and (as I showed you) I used Wolfram Alpha, which used whatever numerical method it chose (and shows the same graph).

What kind of answer do you need (as opposed to wish for)? If WA didn't give a formula, I can't either.

Thanks for your help. However, instead of using Wolfram Alpha I am trying to solve it using a hand held scientific calculator only. What happens after

. How do we proceed from this step forward. I know I sound totally out of my depth posing this question. Many thanks for your help in advance.

 

[topsquark]

Thanks for your help. However, instead of using Wolfram Alpha I am trying to solve it using a hand held scientific calculator only. What happens after

. How do we proceed from this step forward. I know I sound totally out of my depth posing this question. Many thanks for your help in advance.

That depends on a couple of things. What kind of calculator? Are you trying to use a built in function? Or are you using some kind of search algorithm?

-Dan

 

[Steven G]

Thanks for your help. However, instead of using Wolfram Alpha I am trying to solve it using a hand held scientific calculator only. What happens after

. How do we proceed from this step forward. I know I sound totally out of my depth posing this question. Many thanks for your help in advance.

x^2+4.7619log(1-x) = 0 has an obvious solution. That solution is x=0. That is because both 0^2=0 and 4.7619log(1-0) =4.7619log(1)=4.7619*0=0.
How did the original equation change to this equation? Might you have rounded off somewhere?