Solution of exponential equation

[techiejan]

How does the given equation:
βe^(x/β)-x = β+(A/B)

solves to x = √(2A/βB) when β is large?

 

[grzz]

Expand e$^{\frac{x}{\beta}}$ to the first three terms.

 

[techiejan]

Thanks grzz, I solved it now. Can you please tell me the logic behind expanding the exponential to first three terms?

 

[grzz]

The expansion of e$^{\frac{x}{\beta}}$ consists of powers of $\frac{x}{β}$.

Since β is large (compared with x) then we can include only the first three terms of the expansion since the other terms would be very small and would not change the value of x.

Of course, if one wants a more accurate value of x, one must include more terms in the expansion.

 

[techiejan]

Thanks grzz. This was very helpful.