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I need to transpose a formula to solve a problem but I'm not sure on how indices work when under fractions and not integers. The formula is standard air cycle efficency from compression ratio and I need to transpose so I can figure out compression ratio from efficency. I have lambda as air @1.4 so my indice is 0.4
n=1-(1/(r^(l-1)))
I have n so need to transpose for r
Any help greatly appreciated!
need logs?
possibly, how would I apply them?
well, you can get to r^1-l=1-n ?
How would I get to that and how would it help? Really stuck here
n = 1-(1/(r^(l-1)))
1/(1-n) = r^(l-1)
r = (1/(1-n))*(1/(l-1))
log(r) = [log(1/(1-n))]/(l-1)
ok, from where i can see it.
a) (1/(r^(l-1)))= 1-n
b) (r^(l-1))=1/(1-n)
inverse of each side (put 1 over..on each side)
c)1/(r^(l-1))=1-n
1 over a power gives you the same as that power as a negative
d)r^(1-l)=1-n
Perfect, thankyou both! More importantly thanks for the workings, I can see the process now. I do have the value of l so I don't need logs I can just substitute the value in. Gives me a realistic compression ratio of 9.88:1
so.. i think
e) (1-l)log(r)=log(1-n)
so
f)log(r)=log(1-n)/(1-l)