This may be a beginner question, but I can't quite wrap my head around logs… I have a set of data (from an experiment) which gives me an exponential-looking graph (Fig 1). I'd like to "linearize" the graph, i.e. transform the data mathematically, so that the graph looks like a straight line (Fig 2).
The simplest way I can think of is to normalize both x values between x1-x2 (i.e. fit them betweeen 0-1) and y values between y1-y2, and then raise the normalized x to a power to straighten the graph:
f(xnorm)=xnormexp , where xnorm is the normalized x, and exp is some exponent.
My question: can the same effect be achieved using a log function? I.e. can a log expression be applied to x values to "controllably" bring the graph closer to a straight line? Thanks.
Best Answer
Suppose $y=Ae^{kx}$. Then, taking logs, we see that $\log y = kx + \log A$.
Therefore, try taking logs of the $y$-values, and plot those against the ordinary $x$-values. You'll get a straight line whose slope tells you $k$ and whose $y$-intercept tells you $\log A$.