With the priceless help from @tbaumgart I managed to find a solution. Please find attached the final version of the patch.

I have done some more testing and I realized that precision (number of digits after the decimal point) is subject to change. In fact, account balance history chart is pretty straightforward but the code that I worked with is also used with configurable charts in reports. Precision can be changed in the Range tab of the Report Configuration window.
My previous patch created yAxis by calling new KReportCartesianAxis(loc, m_precision) whereas it should be new KReportCartesianAxis(loc, config.yLabelsPrecision()).

0.0 is quite a special argument for the logarithm. I made one last change adding support for this case.

Also there was a todo comment in the code I have removed, so thought it to be appropriate to take care of it lest it be missed out.

/ @todo this might also need some vertical adjustment in case of a horizontal line
/ see below how this has been solved for linear graphs

Indeed, support for logarithmic axis type was required.
Now I think the code is robust and complete. Now I'll just wait for the final review from you :)

Still looks OK to me. Push it.

There is one thing I overlooked in my previous revision. I have just tested my changes against a new account with clear history (empty ledger). It leads to a horizontal-line chart that is drawn incorrectly if no custom grid extension is made. The conclusion is the original grid extension code is here to stay. I have just moved it from void KReportChartView::slotNeedUpdate() to the bottom of void KReportChartView::drawPivotChart( ... ) and I refactored a little bit. Sorry for messing around in this already accepted patch. The good thing is labels are now printed correctly even when one zooms a horizontal-line chart :)

Thank you, @tbaumgart for your time spent reviewing my changes. I have amended my commit message with tag "BUG: 420767"

Do we have a bug entry for this one? If not, please create one and add

Looks good to me.

Uploaded a new diff patch after changes according to @tbaumgart's comments.

This in general is a high quality patch. Thanks much. The changes I suggest are minor details.

Done and branched, no more freeze.

Finally ready for a release.
Plan is:
String freeze from today. (only a coule of strings)
Release Tuesday 21.