How to convert a mel spectrogram to log-scaled mel spectrogram
I think you're wrongly interpreting what the authors meant by log-scaled. When the authors mention log-scaled, they are not referring to the frequency (y) axis, although spectrograms are typically log-scaled here. They are instead referring to the scale of the 3rd dimension in the spectrogram. In your case, the raw spectrogram is displaying power in color. What you want is instead decibels, which are log-scaled.

In your case, the code would look like this:

y, sr = librosa.load('audio/100263-2-0-117.wav',duration=3)
ps = librosa.feature.melspectrogram(y=y, sr=sr)
ps_db= librosa.power_to_db(ps, ref=np.max)

lr.display.specshow(ps_db, x_axis='time', y_axis='mel')


Note: Each spectrogram will be scaled based off of the ref within librosa.power_to_db. If you do not supply anything, librosa just shoves a 1 in there, which may or may not be what you're looking for. You can also try out np.median.