1. Understanding concepts

What is log x?
What is log y?

for y=ax^n why is it appropriate to plot: log x vs log y?
for y=Ae^kx why is appropriate to plot: x vs log y?

ambient room temp:25
e.g data
time x=0,2,4,6,8,10....
temp y=76,72,64,59,55,52...
difference of temp from ambient temp: 51,47 39,34,30,27 ...

Can anyone explain simply?
please anyone help I really need to understand this (it means alot as this is the end of school year)
Any help would be greatly appreciated

Maths help 246

2. Re: Understanding concepts

Hey Mathshelp246.

Taking logs of both sides shows how something change exponentially.

If something is exponentially increasing then a log plot will show a straight line with a positive gradient. If it is exponentially decreasing, then it will be a straight line with a negative gradient.

If something is sub-exponential then the line will be very flat and usually have some kind of asymptote (like a horizontal one).

3. Re: Understanding concepts

Ohh I think I might be getting what you mean!?

why you take log x vs log y - it is a straight line (linear) it is showing how both x and y change exponentially- both are the same (a log of each x and y was taken)
Where as when it is x vs Log y - is at every x value, there is a exponential change in y (i.e. log y)- eventually y will level off, therefore the curve will have an asymptote line for the varible temp (y)

Is this what you mean?

** also if its not too much trouble is: log y the "difference of temperature from ambient room temperature"?**
Thank you so much
means alot ...^_^...

4. Re: Understanding concepts

Basically what I mean is that the slope of the line tells you how its changing on a log scale.

If its a positive slope its changing exponentially in a linear fashion. If its close to flat though it means its changing in a polynomial manner (or sub exponential way).