Log vs. linear frequency scales of Fourier and wavelet transforms
And FFT can be considered a filter bank. The bandwidth of each filter is inversely proportional to the length of the FFT. The width of each filter sets the spacing such that there isn't either too much overlap or gaps between filters.  In an STFT spectrogram, the window width is fixed for the entire FFT, thus the filter spacing is fixed, which turns out to be a linear spacing.

With wavelets the length of each wavelet, being individually adjustable, can be shorter for the higher frequencies, thus have a wider bandwidth, which allows them to be spaced further apart in frequency without leaving gaps between them in the frequency response, thus allowing logarithmic spacing.