Logarithmic fourier transform(LFT) on audio signal
The simplest and most pragmatic solution is to use a normal FFT of a sufficiently large size that you get the required resolution at the lowest frequency of interest. E.g. if you want 1 Hz resolution at the lowest frequency of interest then you will need a 1 second FFT window, i.e. the FFT size would need to be equal the sample rate, e.g. 44100.

Note that even if you could implement a logarithmic FFT then it would still be bound by the laws of physics (information theory) and you would still need a similar length sample window - all you would gain would be convenience (not having to aggregate output bins) at the expense of performance.