How to calculate the value n in this way?

[alternativess]

S=14.5, Q=4.58,

http://img10.imageshack.us/img10/8713/howtoqp7.png

Using scientific calculator, I can get 'n' approximately equal to 3.

By the way, what is the step process to calculate the value 'n'?

[CraigFL]

You would need to use logarithmic functions to solve for 'n'

[alternativess]

I need a way solve for 'n' without using calculator.

Can you give some details guide or example?

[CraigFL]

32 = 2**n (** signifies 2 to the nth power)

Then log(32) = n * log(2)

therefore, n = log(32) / log(2)


n = 1.5051499783 / 0.301029999566

so n = 5

2 to the 5th power is 32....

now you have to apply it to your formula which may yield some kind of quadratic equation that you have to use more numerical methods to solve...

[alternativess]

I think I get some idea. Thank CraigFL.
But how to solve for this for example when there are two to add?

Example:
http://img135.imageshack.us/img135/8245/solvetw6.png
I get n = 2 from calculator

[alternativess]

I have tried to solve an example but can't get n=2 for my example.
http://img9.imageshack.us/img9/8400/getnop0.png
Please correct me. Thanks.