Solving a Logarithm: Can't Remember How? Try Here!

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The equation x = b/D + a*log(D) presents a challenge for solving D due to its dual role as both a logarithmic input and a factor. It is suggested that solving for D in terms of elementary functions is not feasible. The Lambert W function may provide a solution, but it is not straightforward. Additionally, a Taylor Series expansion is proposed as a potential method for approximation. Ultimately, the consensus is that solving for D is complex and may require advanced mathematical techniques.
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Can't remember how to do this (trying to solve for D):

x = b/D + a*log(D)

Any takers? Or is this impossible?
 
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Additive inverse of b/D;
Multiplicative inverse of 'a';

Not sure if the rest is impossible. I'm stuck, since D is the input of the logarithm function and it occurs as a factor too. Am I forgetting something simple, or is this beyond "intermediate" level algebra?
 
symbolipoint said:
Additive inverse of b/D;
Multiplicative inverse of 'a';

Not sure if the rest is impossible. I'm stuck, since D is the input of the logarithm function and it occurs as a factor too. Am I forgetting something simple, or is this beyond "intermediate" level algebra?


Maybe I can simplify the problem here:

a, b, and c are real numbers, D is greater than zero

c = b/D + a*log(D)

how does one solve for D?
 
One doesn't. Not in terms of elementary functions anyway. It might be possible to solve it in terms of the "Lambert W function".
 
HallsofIvy said:
One doesn't. Not in terms of elementary functions anyway. It might be possible to solve it in terms of the "Lambert W function".

How bout a Taylor Series expansion?
 
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