Can someone please explain log scales/graphs?

Universities Forum Helper

To add to @Meowstic's posts, the log (to the base 10) of a value is simply the power of 10 to get that value, for example:

\log _{10} (100) = 2

since

10^{2} = 100,

so the log of 100 is 2 since you need to 10 squared to get 100.

This is done since the values you have may cover a wide range so it is more practical to use logs of those values instead (so using the example above instead of plotting 0.0001 and 1000000, we can plot instead:

-4, (which is

\log _{10} (0.0001),

since

10^{-4} = 0.0001

),

6, (which is

\log _{10} (1000000),

since

10^{6} = 1000000

)).

Is that more clear?

(edited 4 years ago)

Reply 5

mnot

20

Original post by Anonymous

We need to plot the sizes of dna fragments using a log10 base pairs on the y axis. The problem is I have no idea what any of this means. Where do I even start? I tried looking up videos and found some very simplified versions. Then some girl on my course started talking about using "antilogs" and I am extremely confused. If someone could give me a simple introduction to log scales I'd really appreciate it!

antilog, my new favourite terminology, perhaps these girls are also confused and mean exponential (I dont know why but I found that very funny).

@Meowstic & @simon0 hopefully have cleared up what's actually happening in a log scaled graph.

Reply 6

Thanks guys! That really helped! To clear things up, say if I had a DNA fragment with a size of 4000 base pairs and it moved 20mm down the gel electrophoresis paper, would I just stick the 4000 into my calculator log function and plot that result (3.602...) on the y axis, against the distance on the x axis (so 20mm in this case)?
But when I look up log paper on google, it seems that the y axis scales are all really large, like 100-1000 intervals, so how am I supposed to plot the 3.602?
And still not sure where "exponential" comes in as I've just discovered that I do indeed have to use it. Somehow...?

Reply 7

This is an example we were given, it's apparently a semi log graph but I have no idea how. Because if it was, shouldn't the y-axis be non-linear? Sorry the pic is so small and bad quality, it is like that for me too lol, but along the y axis the intervals are 100, 1000 and 10000. Distance along the bottom. Also, as mentioned above the values are really big. That's like if I just didn't use log at all....?

Reply 8

Biology is not my speciality but judging by your uploaded image and searching for DNA base pair gel electrophoresis semi-log graphs, I am guessing the y-axis is logarithmic but the y-axis labels are the actual numbers rather than the equivalent log value of the actual value.

(Note on the y-axis, as you go up at every set interval the label is 10 times bigger than the previous value below).

Am I correct in this?
(If not then post away).

Reply 9

Original post by simon0

Biology is not my speciality but judging by your uploaded image and searching for DNA base pair gel electrophoresis semi-log graphs, I am guessing the y-axis is logarithmic but the y-axis labels are the actual numbers rather than the equivalent log value of the actual value.

(Note on the y-axis, as you go up at every set interval the label is 10 times bigger than the previous value below).

Am I correct in this?
(If not then post away).

I think so? Pls note that I'm really, really dense and also confused so I'm not too clear myself :confused:

But yeah seems like the y axis is logarithmic (if my definition of logarithmic as meaning an axis' intervals goes up/down irregularly is correct), but then the next issue is .... why do I have to use the log function if the intervals are as you said, the actual numbers? If it helps, I am supposed to be making a "semi-log graph."

Also, I still have no idea where the exponential is supposed to come in, how I'm supposed to use it etc.....

Reply 10

No problems. :smile:

The y-axis is still logarithmic but the individual labels have been replaced by the actual values rather than their log values (it is still a semi-log graph but the only difference is the y-axis labels e.g. Instead of label "3", they use label "1000").

Is that better? :smile:

(edited 4 years ago)

Reply 11

Original post by simon0

No problems. :smile:

The y-axis is still logarithmic but the individual labels have been replaced by the actual values rather than their log values (it is still a semi-log graph but the only difference is the y-axis labels e.g. Instead of label "3", they use label "1000").

Is that better? :smile:

It is! Thank you for your help! So basically, I don’t have to use the log function on my calculator at all?

Reply 12

Original post by Snfkin

It is! Thank you for your help! So basically, I don’t have to use the log function on my calculator at all?

You do need to use the log function since you are plotting distance against log of the base pairs! :smile:

The only change are just the y-axis labels.

(edited 4 years ago)

Reply 13

What I suggest is plot distance (x-axis) against the log of the base pairs (y-axis) and plot all those points.

Then after, change the y-axis labels to their normal numbers (so "2" goes to "100", "3" goes to "1000" etc.).

(edited 4 years ago)

Reply 14

Original post by simon0

What I suggest is plot distance (x-axis) against the log of the base pairs (y-axis) and plot all those points.

Then after, change the y-axis labels to their normal numbers (so "2" goes to "100", "3" goes to "1000" etc.).

Thank you so much :smile:

Just finished my graph

Reply 15

Original post by Snfkin

Thank you so much :smile:

Just finished my graph

Great, the method I mentioned was based on my judgment but I have no experience in this myself so there may be some details I may have missed out.

However, does your graph look fine or can it be confirmed to be done correctly?

Reply 16