Hello wirefreeA very brief answer would be that a log-log plot is useful if you think you may have a function of the form

and you want to find out (a) whether this is so; (b) if so, the values of and .

If we take logs of both sides:

, using the laws of logarithms.

Thus, if the functionisof the form , the log-log plot will produce a straight line graph, whose gradient gives the value of , and intercept the value of . (So if the base of the logarithm is 10, and the intercept is , the value of is given by .)

Other applications include the investigation of functions that are themselves logarithmic in nature - the bel and decibel for the measurement of acoustic power, for example.

Here's the Wikipedia article (which perhaps you've already looked at!): Logarithmic scale - Wikipedia, the free encyclopedia.

I can't think of any others that would be useful!If yes, which functions other than log should be considered?

I hope that helps to shed a little light.

Grandad