Question

if I have a graph of several exponential functions, what will a logarithmic scale of the y-axis show me?

Answer 1

Well, if y = C exp(ax), i.e., y an exponential function. Then if now take the log of the y-axis, we have
\[\ln y = \ln C + a x\]

And that is the equation of ... what?

Answer 2

So be absolutely clear, write y' as the new y axis (not the derivative).

Then y' = ax + c, where c = ln C.

What does the graph of that look like?

Answer 3

this will look like a linear function, but I'm actually more interested in what a logarithmic scale will tell me about the relation of the exponential functions

Answer 4

if the slope of one function (in log scale) is smaller than another, will this mean that the exponent of that function is smaller than the one with a higher slope?

Answer 5

The slope of the lines is now the index in the exponential, and the y'-axis intercept is the constant.

So if you have two lines that are parallel, they must have the same index in the exponential.