I'm working on a problem where I have to deal with a loglog scale.
The datapoints on the loglog scale look like polynomials of 3rd degree (if it was on a normal scale).
I've found out that to make a strait line on a loglog scale you use a funktion like f(x) = x^m*10^b as the equivalent to the normal line of f(x) = m*x b
My Question is: How do I make a funktion on a loglog scale that is the equivalent to f(x) = m_1*x^n m_2*x^(n-1) ... m_(n-1)*x m_n
I haven't found anything on the internet in my search so far.
CodePudding user response：
First notice:
log(10^b) = b
log(10^(a log(x)^k)) = a log(x)^k)
Now use:
g(x) = (10(an log(x)n))(10(an-1 log(x)n-1))(10(an-2 log(x)n-2))...(10(a1 log(x)))(10(a0))
which can also be written as
g(x) = 10an log(x)n an-1 log(x)n-1 an-2 log(x)n-2 ... a1 log(x) a0
If you take the log of both sides you will get:
log(g(x)) = an log(x)n an-1 log(x)n-1 an-2 log(x)n-2 ... a1 log(x) a0