Thread: Understanding log and semi log graphs...

Hi I am not too sure on semi log and log graphs

If you were to describe a semi log graph,
where log killing time is on the y axis
and temp. is on the x axis

and as temperature increased, log killing time decreased

how would you describe it?

would you say killing time decreased (dramatically??) as temp increased??

Also how would you describe a graph where both sides were log??

Thanks in advance.

log.jpg

homework of some sort?

kinda, I have an exam next week and I'm studying sterilisation, they use semi-log graphs to explain the activity of disinfectants but I am not quite sure of log and its applications...

so, specifically, the vertical axis is the logarithm of the killing time for some disinfectant at a given temperature?

Yes, vertical axis shows log killing time vs temperature on horizontal axis.

I am studying what affects disinfectants and to what extend.

the graph shows how temp affects the log killing time, all i want is to understand the log bit as I am not too sharp on logarithms.

I'm not asking you to do my homework, just asking for clarity in one area where I am lacking.

it may help you knowing that means and means

This means that as y decreases, x will decrease at an exponential rate.

so as temperature increases, killing time will decrease exponentially?

so we are using semi log paper because one variable changes too vastly to be shown on normal graph paper? is it??

If it was for example Log killing time vs. Log conc. with similar decrease in activity of disinfectant,
would that mean that as you increase conc. exponentially you see a linear decrease in killing time?

the use of the logarithm function isn't so much to save space as show the linear correlation where it exists. It is useful in creating an ideal graph. As temperature increases, the killing time decreases exponentially, which means if you increase the temperature by, for example, 10 degrees, the killing time will be halved. another 10 degrees halves it again, and so on and so forth. It will never theoretically reach 0 in a truly logarithmic graph, but it isn't supposed to since the graph shown is only a snipet, with the ineffective and the point where temperature alone would render the disinfectant pointless are cut off, since they don't fit on the graph anywhere.

if the graph was linear for 2 logarithmic functions, then that shows (provided the logs are equivalent) the two variables linearly correlated.

Ok think I get it now, we use semi log paper to show a linear correlation as we wouldn't get one otherwise. Just a quick question, is there any way of knowing when to use semi log paper? Also, probably a silly question but how do you know killing time is halved if temperature is increased by 10? Thank you so much for your help on this.

the number 10 was arbitrary, but there will be a positive correlation like that. A linear change in one variable will yield an exponential change the other. That's the ear mark of a logarithmic correlation. If one doubles, or triples, or goes up by any multiple at regular intervals for a change the other variable, then its a semi-logarithmic relation between the two, and putting the exponentially changing variable in a logarithm should make a linear relationship.

That is brilliant. Thank you very much for your help it is much appreciated. Hopefully that will come up in my exams now....

Originally Posted by bashy

That is brilliant. Thank you very much for your help it is much appreciated. Hopefully that will come up in my exams now....

For a graphical explanation see http://www.science-site.net/logcalc.htm/ . It is shown how you can calculate logarithms without a calculator by just remembering one number. It give you a good view or aspect of logarithms. Very hand for engineers who use decibel terms.

Originally Posted by arcane

if the graph was linear for 2 logarithmic functions, then that shows (provided the logs are equivalent) the two variables linearly correlated.

quibble: I'm not sure you meant that the way it reads? It could be misunderstood. The graph of ln(y) = 2ln(x) would be straight line with log/log scaling, but that is not a linear correlation of x and y.