Solve for x (multiplication of trigonometric function and logarithmic function)

[brianz24]

Solve for x in terms of y (trigonometric function x logarithmic function)

y = 1.6log₁₀(x)*cos((4*pi*x)/(4.4+pi))*cos((10*pi*x)/11)

I have this equation from a model that I am trying to implement to my project.
However, the equation is too complex I need help from experts

 

[Deleted member 4993]

y = 1.6log10(x)*cos((4*pi*x)/(4.4+pi))*cos((10*pi*x)/11)

I have this equation from a model that I am trying to implement to my project.
However, the equation is too complex I need help from experts

What help do you need - that a calculator cannot give you?!

 

[brianz24]

Find x in terms of y

What help do you need - that a calculator cannot give you?!

I need to isolate the variable x. I tried wolframalpha for this equation - no luck, it plots the graph but does not show the solution for x.

 

[Steven G]

y = 1.6log10(x)*cos((4*pi*x)/(4.4+pi))*cos((10*pi*x)/11)

I have this equation from a model that I am trying to implement to my project.
However, the equation is too complex I need help from experts

By 1.6log10(x) do you mean 1.6log₁₀(x) or 1.6log₁₀[10(x)]. In either case, I do not think that you can solve this equation for x in terms of y.

 

[brianz24]

By 1.6log10(x) do you mean 1.6log₁₀(x) or 1.6log₁₀[10(x)]. In either case, I do not think that you can solve this equation for x in terms of y.

log10 is log₁₀

The thing is I need to solve for x so I could write the program that calculates the parameter straight-forwardly.

If it is unsolveable, then I might try another method to solve this one.

Please let me know if anyone thinks otherwise.

 

[Deleted member 4993]

log10 is log₁₀

The thing is I need to solve for x so I could write the program that calculates the parameter straight-forwardly.

If it is unsolveable, then I might try another method to solve this one.

Please let me know if anyone thinks otherwise.

As far as I can tell the original equation cannot be inverted in closed form. The roots can be "approximated" by using different numerical methods (e.g. Newton's method)

 

[brianz24]

As far as I can tell the original equation cannot be inverted in closed form. The roots can be "approximated" by using different numerical methods (e.g. Newton's method)

I found Maclaurin series to be an option. Currently working on it.

If there is better solution than this, please do tell.