Solving for x in a·(c·e^(1/(d+x·e))-b)=a

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kajakkajak
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Hi I need to solve this equation: $$ a = x \cdot \left( c \cdot e^{ \frac {1} {d+x \cdot e }} - b \right) $$ for x. Unfortunately Wolfram Alpha refused to compute it. Maybe I need a Pro version. Can anyone help me? Thanks!
 
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kajakkajak said:
Hi I need to solve this equation: x*(c*(exp^(1/(d+x*e)))-b)=a for x. Unfortunately Wolfram Alpha refused to compute it. Maybe I need a Pro version. Can anyone help me? Thanks!
Welcome to the PF. :smile:

Is this question for schoolwork? If so, please re-post it in the Homework Help section of the PF, and show your work toward the solution.

If not, can you say where the equation came from? Also, it would help if you would post math questions using LaTeX -- there is a tutorial under INFO, Help at the top of the page. :smile:

EDIT -- I see you edited your post to change the equation to LaTeX form -- Thanks!
 
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Let ##y=\frac{1}{d+ex}## and try to slve for ##y##.
 
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kajakkajak said:
Hi I need to solve this equation: $$ a = x \cdot \left( c \cdot e^{ \frac {1} {d+x \cdot e } - b \right) $$ for x. Unfortunately Wolfram Alpha refused to compute it. Maybe I need a Pro version. Can anyone help me? Thanks!

Is the "e" in "d + x \cdot e" the same "e" in e^{...}?
 
Hmm... an equation of the form

##a=x*e^x##

has a solution with Lambert function:

##x=W(a)##

so I guess the solution is some variation of that theme?
 
fbs7 said:
Hmm... an equation of the form

##a=x*e^x##

has a solution with Lambert function:

##x=W(a)##

so I guess the solution is some variation of that theme?

Unfortunately, that does not seem to work. It looks like either some type of approximation scheme is needed, or else a numerical method when numerical parameter values are given.