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

[vaxop]

without using a calculator's graphing or equation solver tools

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 can't i do these.. i feel like I am missing a basic technique that can be applied to all of these

 

[vaxop]

is it possible?

 

[vaxop]

bumpbumpbump

 

[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.

 

[Tide]

Are you sure you typed your first equation correctly?

 

[arildno]

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

 

[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?

 

[arildno]

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