Got an equation that I am struggling to rearrange to find the value of F. I have tried numerous time to no avail!
59dB = 20log(1 / ( (1+(F/Fc)^6)^0.5) )
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Got an equation that I am struggling to rearrange to find the value of F. I have tried numerous time to no avail!
59dB = 20log(1 / ( (1+(F/Fc)^6)^0.5) )
SOLVED IT!
59dB = 1 / (1 + (F/Fc)^6)^0.5
F = Cubetr(10^(59/20) x 1^0.5 x Fc^3 - 1)
I can simplify this for you ,but there is a fundamental problem here - the denominator of the log exprssion must be less than 1 (since the log of 1/denominator has to be greater than 1). But that means that (F/Fc) ^ (1/6) must be negative. And that can't be. So I suggest you go back and check that you wrote the equation correctly.
However, if you want to go through the simpliifcation process anyway, here are the details:
Start with:
59dB = 20log(1 / ( (1+(F/Fc)^6)^0.5) )
Divide both sides by 20:
59/20 = log (1 / ( (1+(F/Fc)^6)^0.5) )
Using the definition of logarithms:
10^(59/20) = 1 / ( (1+(F/Fc)^6)^0.5)
Square both sides:
(10 ^ (59/20))^2 = 10 ^ (108/20) = 1 / (1+(F/Fc)^6)
Take the inverse:
1+(F/Fc)^6 = 10 ^ -(108/20) = 1/(10^(108/20))
Massage:
(F/Fc)^6 = 1/(10^(108/20)) -1
F/Fc = (1/(10^(108/20)) -1)^1/6
F = Fc * (1/(10^(108/20)) -1)^1/6
Or, perhaps clearer:
At this point you see the problem clearly - the quantity that you're trying to take the sixth root of is negative!
You seem to have changed the equation you are trying to solve - is it supposed to be this:Quote:
Originally Posted by Spike1984
Please confirm.
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