How Do You Solve the Sonar Range Equation Using the Lambert W Function?

[zibifnik]

Hello,

Trying to solve an equation about sonar range equation and can not end up with a feasible solution.

The equation to be solved for x is as follows;

10*log10(x) + a*x = b

Any idea/suggestion/solution will help a lot.

 

[HallsofIvy]

You are not going to get any simple solution to that. You might be able to get a solution in terms of the "Lambert W function". It is defined as the inverse to the function xe^x.

 

[zibifnik]

My first solution for the equation

$$10\log10(x)+ax = b$$ via Lambert W function was

$$x = \frac{4.35}{a} * LambertW(\frac{a}{4.35}\exp(\frac{b}{4.35}))$$

I tested it again. It gives the correct results.

Thanks a lot.