Simple equation, but I dont know how to solve for x

1. Jun 4, 2006

vaxop

without using a calculator's graphing or equation solver tools :tongue:

2000x^16 + 5000x^39 = 3000 + 1600x^12
how can i solve for x?

200(1+i)^7 + 100(1+i)^5 = 300(1+i)^3
i?

1.06^t = 2(1.04)^t
t?

1.08^-n + 1.08^-2n = 1
n?

6x^2-2x-3=0
argh why cant i do these.. i feel like im missing a basic technique that can be applied to all of these

Last edited: Jun 4, 2006
2. Jun 4, 2006

vaxop

is it possible?

Last edited: Jun 4, 2006
3. Jun 4, 2006

bumpbumpbump

4. Jun 4, 2006

arildno

As for the second, i=-1 is a solution.
To find the other solutions, divide throughout with (1+i)^3, and introduce z=(1+i)^2.

5. Jun 4, 2006

Tide

Are you sure you typed your first equation correctly?

6. Jun 4, 2006

arildno

I was also wondering about that one.
It is order of magnitudes more difficult to solve than the others.

Last edited: Jun 4, 2006
7. Jun 4, 2006

vaxop

how about if the unkown is in the exponent
like..
1.06^t = 2(1.04)^t
t?

1.08^-n + 1.08^-2n = 1
n?

8. Jun 4, 2006

arildno

Use well-known logarithm rules for the first one, set $x=1.08^{-n}$ in the second one.