Mathematics Brain Freeze

Power law, the slope give the exponent.

George H.

It is a linear function.

y = x^a

Slope of the line is log_10(a)

(a can be positive or negative).

Time to move over to sales?

Y=X obviously plots as a straight line!

It's not so simple - there are two parameters:

y = b * x ^ a.

straight line y=m*x + b y=LOG(Y) and x=LOG(X) means LOG(Y)=m * LOG(X) + b

Y= X^m * 10^b or Y=k*X^m

The b just turns into an offset. ln(b*x^a) = ln(a)*x + ln(b)

George H. (I love log-log plots!)

Once I tried asking for log-log paper in a college bookstore - I was told in no uncertain terms that no such thing exists.

For a=2 :

octave-3.2.4:1> x=linspace(0,100,10); octave-3.2.4:2> y=x.^2; octave-3.2.4:3> putenv('LINES','30'); octave-3.2.4:4> putenv('COLUMNS','70'); octave-3.2.4:5> putenv('GNUTERM','dumb'); octave-3.2.4:6> plot(x,y)

On Fri, 29 Apr 2016 11:13:36 -0700, Jim Thompson Gave us:

Roll it up and use it as a LOG LOG to start your fireplace with.

OR LOG It's better than bad, it's good!

I spent 10 minute with EXCEL. This is actually an interesting question and the answer is surprising.

if we take functions of the form

y = ax^3 + bx^2 + cx + d

the following ALL plot as a straight line on a log log plot

a,b,c=0 and d= constant offset only a,b,d =0 and c = constant slope (linear with NO offset) a,c,d=0 b= constant (pure square law) b,c,d,=0 a = constant (pure cubic)

So it seems the general rule would be that i a function plots as a straight line on a log log plot IFF all terms are = 0 EXCEPT one and only one = a constant. If more than 1 coef >0 then the line is not straight.

I would have never guessd that! I'm sure someone will check this to be correct or not.

Mark

I see this is the same result as Don K.

His is more general.

I am saddend that my HP prime does not do log-log. It would have been easy.

But the wiki says

log_10 F(x) = m log_10 x + b, F(x) = x^m X 10^b, where m is the slope and b is the intercept point on the log plot.

Cheers

What you have done it to find all the cases of the quadratic formula where the function is a simple power relationship, y = x^z, with different values of z = 0, 1, 2 and 3. Add more terms to your original polynomial and you will find this rule extends. z does not need to be an integer.

Yes, of course. If you plot y=x on log-log axes you get a straight line just as if you plot y=x on linear axes.

And that's just the equation of a straight line on log-log.

Any gain Bode plot far from zeros and poles? Perhaps also Laplace transforms of transfer functions with delays?