Proving an exponential relationship

If time is not a variable do you still end up with a graph of natural log whatever against the other variable

Yes, you do.

Thank you!

Physics A2
I know how to prove that something is exponential with regards to time (graph of natural log whatever against time gives a negative gradient with +ve y intercept. I have only ever seen these exponential relationships with time and the notes my teacher gave just say "to prove something is exponential take logs of values". If time is not a variable do you still end up with a graph of natural log whatever against the other variable or do you take logs of both variables?

Thank you!

Just be careful because that negative part proves exponential decay. The gradient could be positive if it were an exponential growth (e.g. in a capacitor charging up)

Also as a quick tip, remember that in physics, the units for log(dimension) are the same as the units of the actual dimension. I know it seems weird but for example ln(time), where time is measured in seconds, would still be measured in seconds. You must remember this when labelling graphs!

So it's not In(seconds) ???

Nope.

Unit is seconds

Why?

I mean, time^2 is measured in seconds^2 ... ???

Yes because that's [time] * [time]. Ln is a function

Oh

and is it L n or I n?

y'know as in 'in'

do you say 'in 3'???

Lower case L.

Can be pronounced "lun" or "L.N.", however you want to.

So when I wrote 'in' on my ISA, I am going to lose a mark?

you dotted your i?

No, I did capital I withn lines at the top and bottom

That'll be fine. It's how some people draw their lower case Ls anyway