You chart looks correct. The axis displays the original values - TAChart calles them "axis coordiates", but the marks are plotted in an invisible coordinate system defined by the logarithms ("graph coordinates"). So, when the y value of your data is 100 the displayed "axis coordinate" is 100, but the "graph coordinate" is log10(100) = 2.
I understand your question such that you do not want the axis to be labelled with the "axis" values , e.g., 1, 10, 100, 100, but with their logs, 1, 2, 3, the "graph" values.
This is not done by the axis transformation.
If you want to have logs on the axis you must calculate the logs by yourself, and must NOT use an axis transformation. -- see the second chart in the attached modified project.
Please note that fitting to data have a different meaning in both cases. Suppose your data follow an exponential function (y = exp(x)). When you use a log axis transformation the correct way to fit thiese data with a TFitseries is by setting FitSeries.FitEquation to feExponential - this will result in a straight line in the log chart.
However when you plot precalculated logs and do NOT use an axis transformation you must use FitEquation = felinear to get a straight line.