Wikipedia:Reference desk/Archives/Mathematics/2015 September 8

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September 8

Need some literature about converting an exponential function to a linear representation

Need literature, above high-school level, but introductory. Given a function is in the form y = ax^2, and want to convert into a linear function, and plot it (i.e. log(y) = 2log(ax). Or function is in the form y = ax^2 + b and cannot apply the previous operation, but other means might be possible. Basically, how and when to convert into a linear function something that is exponential. --Yppieyei (talk) 12:04, 8 September 2015 (UTC)

Have you read Log–log_plot? You're not really changing the essence of the function, you're just changing the way you plot it. Or you could think of it as a mapping from functions of the form y=ax^2 to functions of the form Y=mX+b, via X=log(x). But the original function is still exponential nonlinear, and the target function is still exponential nonlinear in terms of x.

You might already know this, just wanted to link a relevant article. Is there something more specific you'd like to know? E.g. you can still plot y=ax^2+b on a log-log plot, and you can use List_of_logarithmic_identities#Summation.2Fsubtraction to handle the log of the sum if you want to do further algebraic manipulation. SemanticMantis (talk) 14:22, 8 September 2015 (UTC)

Log is a group homomorphism between the positive reals under multiplication and the reals under addition (i.e., log(ab)=log(a)+log(b)). If you want to get a sum of things after applying log, you should begin with a product of things. --JBL (talk) 14:52, 8 September 2015 (UTC)

Side note: If y = ax², then log(y) = log(a) + 2log(x). Only if y = (ax)², then log(y) = 2log(ax) = 2log(a) +2log(x). Abecedare (talk) 15:15, 8 September 2015 (UTC)\

Right, y = ax^2 and y = (ax)^2 are not the same.

I'm not just after a wikipedia article, even if these are good links, but published material. Something like [1], which would be an ideal choice, were it published yet. --Yppieyei (talk) 15:19, 8 September 2015 (UTC)