Test for Logarithmic Graph

Is there a test you can use to see if a graph is logarithmic?

For example, to test for an exponential decay graph there is the half-life method.

If (a,b) is any point on the graph then (a^2, 2b) should also be on the graph ?

That doesn't seem to work on my graph. Perhaps it would be best if I showed you my data and graph.

That doesn't seem to work on my graph. Perhaps it would be best if I showed you my data and graph.

Well that certainly doesn't look much like a logarithmic graph. It' s almost a straight line

Assuming air resistance is negligible it'd be a straight line, but eventually if you get high enough it will level off (which would be terminal velocity)

The graph is of exit velocity of water from a spouting cylinder against height of water level.

I am meant to analyse this graph but don't really know what to say. I thought at 0.2m and less it is tending towards the origin so assumed it was closer to a log graph than a straight line.

The graph is of exit velocity of water from a spouting cylinder against height of water level.

I am meant to analyse this graph but don't really know what to say. I thought at 0.2m and less it is tending towards the origin so assumed it was closer to a log graph than a straight line.

Well it's like log graph, but at what base.

How many marks for analysis?

a log graph does NOT tend to the origin

You can test if a graph is logarithmic by testing coordinates. If the graph is logarithmic, then $\frac{log y}{x}$ will be equal (or close) to a constant for all coordinate sets.