OpenEuphoria

Re: Algebra problem

• Posted by "Juergen Luethje" <j.lue at gmx.de> Jul 07, 2005
• 597 views

Derek Parnell wrote:

> My high school algebra has deserted me 
>
>  Given the formula
>
>    A^b + Cb = d
>
> how do I solve for 'b'?

Just for the sake of clarity, I assume you mean the same as:
    A^b + C*b = d ,
right?

This is not simple, because b is not only exponent of A, but also
factor of C.

If we know the values of A, C, and d, we can go the following way:
Change the equation to
    A^b = -C*b + d

Plot the graphs of the two functions
    f(b) = A^b
    g(b) = -C*b + d

The b values of all points where both graphs intersect are solutions
of the original equation.

( Note:
  It is not actually necessary to plot 2 functions.
  We can also e.g. change the equation to
    A^b + C*b - d = 0 ,

  then plot the function
    f(b) = A^b + C*b - d

  and look for the points where the function graph intersects with
  the x-axis. )

                   -----------------

Example for
    A = 2
    C = 3
    d = 5

The equation to solve is then (using x instead of b, because the program
that I used for plotting only "knows" x):
    2^x + 3*x = 5

The two functions are then
    f(x) = 2^x
    g(x) = -3*x + 5

On the plot at <http://home.arcor.de/luethje/temp/equ.jpg>, we see that
there is one intersection at x = 1.

I hope someone else knows a simpler and more general way ...

Regards,
   Juergen


PS: Rob, I wanted to upload the "attachment" to www.rapideuphoria.com
   (as you once have offered). But I forgot the name of the directory,
   where the file then is. Maybe you can add some short instructions to
   the page <http://www.rapideuphoria.com/cgi-bin/usercont.exu?dbId=new>?