Question 20113: i have a logarithmic graph ......... how do i find the equation?
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! do you mean that y axis is plotted on log scale and x axis is plotted on normal scale..or both x and y axis are plotted to log scale ,the folowing example will help to understand
let us take an example..let the graph be a straight line while plotted on log scale for y axis and normal scale for x axis set of data could be
x.....1....10.....100......1000......10000....etc
log x.....0.....1.......2........3..........4....etc...
y.....10....1.......1/10.....1/100.......1/1000...etc...
log y..1....0........-1.......-2............-3......
while taking a scale of 1 cm as 1 unit you will find that in log graph ,if there is 1 at 0 cm,the next point after 1 cm will show 10 , and the next point after another cm will show 100 ,the next point after another 1 cm will show 1000 , and the next point after another cm will show 10000...etc..that is ineffect they are log 1 at zero cm,log 10 at 1 cm ,log 100 at 2 cm ...etc...
hence if we get a straight line on such a plot ...that means really ,assuming both axes are plotted to lg scale,log x is linearly related to log y...or
log y =m*log x+log c...where m is the slope of the line and log c is the y intercept of the line ..drawing comparison from linear scale plots wher we call the eaqn.as y=mx+c
so on a log plot instead of y=mx+c we have log y = m log x +log c
that is using log formula...log x*y=log x +log y,and a log x = log (x^a)we get
log y =log (x^m)*c
y=(x^m)*c...is the real eqn.without logs ..so the key is take the log given graph ...see its pattern and make the eqn in normal manner and finally replace x with log x and y with log y to get the real relation ship..simplify if neede as above to get eqn. without logs.
hope it is clear if you have any difficulty please come back ...
|
|
|
