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# Exponential Equation watch

1. Is there a way to get an exact answer to:

0.75n + 1 = (4/3)n ?

Thanks.
2. (Original post by Simba)
Is there a way to get an exact answer to:

0.75n + 1 = (4/3)n ?

Thanks.
I cant find any solutions to that, have you typed it up right?
(or it could be way past my understanding of maths )
3. Well, there appears to be a solution around 1.675... but I would like it as an exact fraction, and I'm not sure how to work it out as an exact fraction ...

Thanks anyway ...

~~Simba
4. (Original post by Simba)
Is there a way to get an exact answer to:

0.75n + 1 = (4/3)n ?

Thanks.
You can re-write the above equation in the form:

X + 1 = X^-1

where X = 0.75^n. This can be rearranged into:

X^2 + X - 1 = 0

You can do the rest.
5. Thanks !

I'm left with 0.75n = (-1 ± √5)/2

So nlog0.75 = log[(-1 + √5)/2]

n = log[(-1 + √5)/2]/log 0.75

So how do I get 'n' as an exact fraction *Rubs head*?
6. I think n is irrational.

The answer may very well be irrational anyway.
8. Ok, thank you ... I was expecting the answer to be rational; otherwise (4/3)n will be irrational... but, never mind ...

Thanks,

~~Simba

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