Solving a logarithm

[natgbz]

Main Question or Discussion Point

Can't remember how to do this (trying to solve for D):

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

Any takers? Or is this impossible?

 

[symbolipoint]

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?

 

[natgbz]

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?

 

[HallsofIvy]

One doesn't. Not in terms of elementary functions anyway. It might be possible to solve it in terms of the "Lambert W function".

 

[natgbz]

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?