System of 2 equations

[AvgStudent]

I don't know why I'm having trouble solving this system of equations.
[math]230.857=\theta(0.1^{-1/\alpha}-1)\\ 728.318=\theta(0.01^{-1/\alpha}-1)\\[/math]
I tried dividing equation 1 by equation 2, which give me...
[math]0.317=\frac{0.1^{-1/\alpha}-1}{0.01^{-1/\alpha}-1}[/math]
Thought about taking the log on both sides but that wouldn't help me either. Ideas?

 

[Deleted member 4993]

I don't know why I'm having trouble solving this system of equations.
[math]230.857=\theta(0.1^{-1/\alpha}-1)\\ 728.318=\theta(0.01^{-1/\alpha}-1)\\[/math]
I tried dividing equation 1 by equation 2, which give me...
[math]0.317=\frac{0.1^{-1/\alpha}-1}{0.01^{-1/\alpha}-1}[/math]
Thought about taking the log on both sides but that wouldn't help me either. Ideas?

Use a standard equation from ratios: If

\(\displaystyle \frac{a}{b} \ \ = \ \frac{c}{d}\) ......................................then

\(\displaystyle \frac{a - b}{a + b} \ \ = \ \frac{c - d}{c + d}\).........................it can be proven fairly easily

after that it is simple algebra.

 

[Dr.Peterson]

I don't know why I'm having trouble solving this system of equations.
[math]230.857=\theta(0.1^{-1/\alpha}-1)\\ 728.318=\theta(0.01^{-1/\alpha}-1)\\[/math]
I tried dividing equation 1 by equation 2, which give me...
[math]0.317=\frac{0.1^{-1/\alpha}-1}{0.01^{-1/\alpha}-1}[/math]
Thought about taking the log on both sides but that wouldn't help me either. Ideas?

Just clear fractions! Multiply both sides by the denominator.

There will be several other hints I could give, but I'll just give the one to start.

EDIT: @blamocur's hint is one of my others, but that alone will take you (almost) straight to the answer.

 

[blamocur]

[imath]0.01^{-1/\alpha} = \left(0.1^{-1/\alpha}\right)^2[/imath]

 

[AvgStudent]

[imath]0.01^{-1/\alpha} = \left(0.1^{-1/\alpha}\right)^2[/imath]

If only I could notice that hehe
Let [imath]x=0.1^{-1/\alpha}[/imath]:
[math]0.317=\frac{0.1^{-1/\alpha}-1}{0.01^{-1/\alpha}-1}=\frac{x-1}{x^2-1}=\frac{1}{x+1}\\ x=2.1544 \implies \alpha=3, \theta=200[/math]
Thanks!