Hi Philipp,
as Alexander stated correctly, the choice of the logarithm just changes the scaling, so it doesn´t really matter which one is used. In this particular case, I assume that the solution was calculate with numpy, where "numpy.log" results in the natural logarithm.
Concerning the exam, either stick to the base given in the task or use the base from the lecture slides. When in doubt, just leave us a note which base you used.
Best,
Benedikt
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