Finding the constants in an expression

[ArnoldEdv]

I have a problem with this formula:

I have two known value series: A1, B1, C1 and A2, B2, C2.
That gives me two equations with two unknowns n and k.

Mentor note:
More readable versions of the two equations:
$$A_1 = \sqrt[n]{\frac{B_1} k + C_1^n}$$
and
$$A_2 = \sqrt[n]{\frac{B_2} k + C_2^n}$$
Does anyone have a clue how to solve this?

 

[fresh_42]

I have a problem with this formula:
View attachment 230078
I have two known value series: A1, B1, C1 and A2, B2, C2.
That gives me two equations with two unknowns n and k.
View attachment 230079 View attachment 230080
Does anyone have a clue how to solve this?

You get a function $k=k(n)$ from the equations and then $A_1^n-C_1^n=\gamma (A_2^n-C_2^n)$ which I assume can only be solved numerically.

 

[mathman]

note: $\gamma=\frac{B_1}{B_2}$.

 

[ArnoldEdv]

Thank you for your answers.
I was hoping that there was some way of solving this equation that I didn't know of.
Probably there isn't.