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Logs: Data Lines
The results of an experiment are plotted on a graph of log10(y) against log10(x), producing a straight line (not shown to scale) with gradient –0.1 and intercept 1.1.
The relationship between y and x is either y = p x q or y = p q x.
Fill in the values of the constants p and q to 3 dps and write x in the other input box to give the relationship between y and x:
y =
log10(y)
log10(x)

tickcross


Worked Solution:

The X–Y graph is a straight line
Y = m X + c with gradient m = –0.1 and intercept c = 1.1.
The Y values are the log10(y) values and the X values are the data log10(x) values.
The straight line in terms of the data values is
  log10(y) = –0.1 log10(x) + 1.1
To simplify this we must write 1.1 as a log to base 10:
101.1 = 12.58925=>1.1 = log10(12.58925)
=>log10(y) = –0.1 log10(x) + log10(12.589)
=>log10(y) = log10(12.589 x–0.1)
=>y = 12.589 x–0.1

© MEI Produced by Dr Ron Knott, revised 18 April 2008
tom . button [AT] mei . org . uk 		Test reference: LogsDataLines.html?ref=45882